This is an English translation of my Japanese blog post submitted to a Japanese googological event. This is a notation based on the side nesting method in Japanese googology. It might include many typos and errors, e.g. undefined behaviours or obvious infinite loops. I appreciate feedbacks.
Summary[]
Faery「This time, I'm gonna create an ordinal notation associated to Veblen hierarchy for y'all!」
Unfortunately, this is a notation not associated to Veblen hierarchy. She tried to create an ordinal notation associated to Veblen hierarchy, but made mistakes in the comarison algorithm and the standardness algorithm. Does it well-founded? I do not know.
Notation[]
I define a recursive set \(T\) of formal strings consisting of \((\), \()\), and \(+\) in the following recursive way:
- \(() \in T\).
- For any \((a,b,c) \in T^3\), \((abc) \in T\).
- For any \((a,b) \in (T \setminus \{()\})^2\), \(a+b \in T\).
I put \(0 = ()\). I define a recursive subset \(PT \subset T\) in the following way:
- \(0 \notin PT\).
- For any \((a,b,c) \in T^3\), \((abc) \in PT\).
- For any \((a,b) \in (T \setminus \{0\})^2\), \(a+b \notin PT\).
For example, \((000) \in PT\) while \((000) + (000) \in T \setminus PT\).
Faery「Variadic Veblen hierarchy smells too complicated, so it's pretty good to start from \(3\)-ary one!」
Ordering[]
I simultaneously define recursive \(2\)-ary relations \(s < t\) and \(s \leq t\) on \(T\) in the following recursive way:
- \(s \leq t\) is equivalent to \(s < t\) or \(s = t\).
- If \(s = 0\), then \(s < t\) is equivalent to \(t \neq 0\).
- If \(s \neq 0\) and \(t = 0\), then \(s < t\) does not hold.
- Suppose that there exist an \((a,b,c) \in T^3\) and a \((d,e,f) \in T^3\) such that \(s = (abc)\) and \(t = (def)\):
- If \(a = d\), then \(s < t\) is equivalent to that either one of the following holds:
- \(b < e\) and \(c \leq t\).
- \(b = e\) and \(c < f\).
- \(e < b\) and \(s < f\).
- If \(a \neq d\), then \(s < t\) is equivalent to that either one of the following holds:
- \(a < d\) and \(c \leq t\).
- \(d < a\) and \(s < f\).
- If \(a = d\), then \(s < t\) is equivalent to that either one of the following holds:
- If there exist an \((a,b,c) \in T^3\) and a \((d,e) \in PT \times (T \setminus \{0\})\) such that \(s = (abc)\) and \(t = d+e\), then \(s < t\) is equivalent to \(s \leq d\).
- If there exist an \((a,b) \in PT \times (T \setminus \{0\})\) and a \((d,e,f) \in T^3\) such that \(s = a+b\) and \(t = (def)\), then \(s < t\) is equivalent to the negation of \(t < s\).
- If there exist an \((a,b) \in PT \times (T \setminus \{0\})\) and \((d,e) \in PT \times (T \setminus \{0\})\) such that \(s = a+b\) and \(t = d+e\), then \(s < t\) is equivalent to that either one of the following holds:
- \(a < d\).
- \(a = d\) and \(b < e\).
Then \(\leq\) forms a total ordering, but does not form a well-ordering.
Faery「Somehow weird... Did I make mistakes...? But I've no idea...」
Standard Form[]
I put \(1 = (000)\). I define a recursive map \begin{eqnarray*} T \times T & \to & T \\ (a,t) & \mapsto & (a00) \times (t) \end{eqnarray*} in the following recursive way:
- If \(t = 0\), then \((a00) \times (t) = 0\).
- Suppose that there exists a \((d,e,f) \in T^3\) such that \(t = (def)\).
- Suppose that \(t < (00(00(a00)+1))\).
- If \(t = 1\), then \((a00) \times (t) = (a00)\).
- If \(d = 0\), \(e = 0\), and \(t \neq 1\), then \((a00) \times (t) = (00(a00)+f)\).
- If \(d = 0\) and \(e \neq 0\), then \((a00) \times (t) = (00(a00)+t)\).
- If \(d \neq 0\), then \((a00) \times (t) = (00(a00)+t)\).
- If \((00(00(a00)+1)) \leq t\), then \((a00) \times (t) = t\).
- Suppose that \(t < (00(00(a00)+1))\).
- If there exists a \((d,e) \in (T \setminus \{0\}) \times PT\) such that \(t = d+e\), then \((a00) \times (t) = (a00) \times (d) + (a00) \times (e)\).
For example, \((100) \times (1+1) = (100) + (100)\).
For each \(x \in T\), I define a recursive subset \(OT_x \subset T\) in the following recursive way:
- \(0 \in OT_x\).
- For any \((a,b,c) \in T^3\), \((abc) \in OT_x\) is equivalent to that all of the following hold:
- \((a,b,c) \in OT_x^3\).
- If \(a = 0\), then \((100) \times (b) \leq x\) and \(b \in OT_{(100) \times (b)}\).
- If \(a \neq 0\), then \((a+100) \times (b) \leq x\) and \(b \in OT_{(a+100) \times (b)}\).
- \(c < (abc)\).
- For any \((s,t) \in (T \setminus \{0\}) \times PT\), \(s+t \in OT_x\) is equivalent to that all of the following hold:
- \((s,t) \in OT_x^2\).
- If \(s \in PT\), then \(t \leq s\).
- If there exists an \((a,b) \in (T \setminus \{0\}) \times PT\) such that \(s = a+b\), then \(t \leq b\).
I put \(OT = \{x \in T \mid x \in OT_x\}\). I call an expression in \(OT\) a standard form expression. For example, \((100)\) and \((100) + (010)\) are standard form expressions, while \((010)\) is not. I expect that the restriction of \(\leq\) to \(OT\) forms a well-ordering.
Faery「The weird comparison perhaps works by restricting additions in standard form expressions!! I WIN!!」
Fundamental Sequence[]
For an \(s \in T\), I denote by \(L(s)\) the length of \(s\) as formal strings. I define a recursive map \begin{eqnarray*} [ \ ] \colon OT \times \mathbb{N} & \to & OT \\ (s,n) & \mapsto & s[n] \end{eqnarray*} in the following recursive way:
- If \(s = 0\), then \(s[n] = 0\).
- If \(s \neq 0\), then \(s[n] = \max \{t \in OT \mid t < s \land L(t) < L(s) + 9n\}\).
By the definition, \(s \neq 0\) implies \(s[n] < s\).
Faery「Setting FSs is awfully tiresome, so I throw it away in this way!」
Large Function[]
I define a recursive map \begin{eqnarray*} (100)_{\bullet}(\bullet) \colon OT \times \mathbb{N} & \to & \mathbb{N} \\ (s,n) & \mapsto & (100)_s(n) \end{eqnarray*} in the following recursive way:
- If \(s = 0\), then \((100)_s(n) = n+1\).
- If \(s \neq 0\), then \((100)_s(n) = \sum_{m=0}^{n} (100)_{s[m]}^m(m)\).
If the restriction of \(\leq\) to \(OT\) is a well-ordering, then \((100)_{\bullet}(\bullet)\) is total.
I define a recursive map \begin{eqnarray*} (100)_{\bullet} \colon \mathbb{N} & \to & OT \\ n & \mapsto & (100)_n \end{eqnarray*} in the following recursive way:
- If \(n = 0\), then \((100)_n = (100)\).
- If \(n \neq 0\), then \((100)_n = ((100)_{n-1}00)\).
The recursive map \((100)_{\bullet}\) gives a limit of the notation system \((OT,\leq)\).
Faery「Finally, I've achieved \(\varphi(1,0,0,0) = \varphi(\varphi(\cdots \varphi(1,0,0) \cdots,0,0),0,0)\), haven't I!?」
I note that her analysis is wrong, because it is not an ordinal notation associated to Veblen hierarchy. I expect that the limit of this notation is an OCF-level if it actually works.
Large Number[]
I submitted the computable large number \((100)_{(100)_{(100)_{(100)}(100)}}(100)\) to the Japanese googological event.
Faery oO(Yeah...! Everyone enjoys my ordinal notation associated to Veblen hierarchy...! Zzz...)
Analysis[]
I show tables of the expectation of the ordinal type \(o(\alpha) \in \Omega\) of the segment \(\{\beta \in OT \mid \beta < \alpha\}\) for an expression \(\alpha \in OT\) without a proof. Since the original system of fundamental sequences is complicated, I exhibit another equivalent system of fundamental sequence, which I will call "modified fundamental sequences" later. Since the analysis of this notation is very difficult for me, the expectation might include so many obvious mistakes. In order to shorten expressions, I employ the following abbreviations:
| expression | Abbreviation |
|---|---|
| \(()\) | \(0\) |
| \((000)\) | \(1\) |
| \(1+1\) | \(2\) |
| \((001)\) | \(\omega\) |
Up to \(\varepsilon_0\)[]
I describe the ordinal types into iterated Cantor normal forms. In this realm, \(o\) preserves the addition. The map \(c \mapsto (00c)\) plays a role analogous to the map \(\gamma \mapsto \omega^{\gamma}\).
| expression \(\alpha \in OT\) | modified fundamental sequence | ordinal \(o(\alpha) \in \Omega\) |
|---|---|---|
\(0\)
|
\(0\)
| |
\(1\)
|
\(0\)
|
\(\omega^{0}\)
\(= 1\) |
\(2\)
|
\(1\)
|
\(\omega^{0}+\omega^{0}\)
\(= 2\) |
\(\omega\)
|
\(0\)
\(1\) \(2\) |
\(\omega^{\omega^{0}}\)
\(= \omega\) |
\(\omega+1\)
|
\(\omega\)
|
\(\omega^{\omega^{0}}+\omega^{0}\)
\(= \omega+1\) |
\(\omega+2\)
|
\(\omega+1\)
|
\(\omega^{\omega^{0}}+\omega^{0}+\omega^{0}\)
\(= \omega+2\) |
\(\omega+\omega\)
|
\(\omega\)
\(\omega+1\) \(\omega+2\) |
\(\omega^{\omega^{0}}+\omega^{\omega^{0}}\)
\(= \omega+\omega\) |
\((002)\)
|
\(0\)
\(\omega\) \(\omega+\omega\) |
\(\omega^{\omega^{0}+\omega^{0}}\)
\(= \omega^{2}\) |
\((00\omega)\)
|
\((000)\)
\((001)\) \((002)\) |
\(\omega^{\omega^{\omega^{0}}}\)
\(= \omega^{\omega}\) |
\((00\omega+1)\)
|
\(0\)
\((00\omega)\) \((00\omega)+(00\omega)\) |
\(\omega^{\omega^{\omega^{0}}+\omega^{0}}\)
\(= \omega^{\omega+1}\) |
\((00\omega+2)\)
|
\(0\)
\((00\omega+1)\) \((00\omega+1)+(00\omega+1)\) |
\(\omega^{\omega^{\omega^{0}}+\omega^{0}+\omega^{0}}\)
\(= \omega^{\omega+2}\) |
\((00\omega+\omega)\)
|
\((00\omega)\)
\((00\omega+1)\) \((00\omega+2)\) |
\(\omega^{\omega^{\omega^{0}}+\omega^{\omega^{0}}}\)
\(= \omega^{\omega+\omega}\) |
\((00(002))\)
|
\((000)\)
\((00\omega)\) \((00\omega+\omega)\) |
\(\omega^{\omega^{\omega^{0}+\omega^{0}}}\)
\(= \omega^{\omega^2}\) |
\((00(00\omega))\)
|
\((000)\)
\((00\omega)\) \((00\omega+\omega)\) |
\(\omega^{\omega^{\omega^{\omega^{0}}}}\)
\(= \omega^{\omega^{\omega}}\) |
\((00(00(00\omega)))\)
|
\((00(000))\)
\((00(00\omega))\) \((00(00\omega+\omega))\) |
\(\omega^{\omega^{\omega^{\omega^{\omega^{0}}}}}\)
\(= \omega^{\omega^{\omega^{\omega}}}\) |
\((100)\)
|
\(\omega\)
\((00\omega)\) \((00(00\omega))\) |
\(\omega^{\omega^{\cdot^{\cdot^{\cdot^{\omega^{0}}}}}}\)
\(= \varepsilon_{0}\) |
Up to \(\zeta_0\)[]
I describe the ordinal types into expressions with epsilon function. From this realm on, the correspondence \(o\) does not preserve the addition. For example, \(o((100)+(100))\) isintended to coincide with \(\zeta_0\), which is much greater than \(o((100))+o((100)) = \varepsilon_0 + \varepsilon_0\). The map \(c \mapsto (01c)\) plays a role analogous to the map \(\gamma \mapsto \varepsilon_{\gamma}\).
| expression \(\alpha \in OT\) | modified fundamental sequence | ordinal \(o(\alpha) \in \Omega\) |
|---|---|---|
\((100)\)
|
\(\omega\)
\((00\omega)\) \((00(00\omega))\) |
\(\varepsilon_{0}\)
|
\((100)+1\)
|
\((100)\)
|
\(\varepsilon_{0}+1\)
|
\((100)+2\)
|
\((100)+1\)
|
\(\varepsilon_{0}+2\)
|
\((100)+\omega\)
|
\((100)\)
\((100)+1\) \((100)+2\) |
\(\varepsilon_{0}+\omega\)
|
\((100)+\omega+1\)
|
\((100)+\omega\)
|
\(\varepsilon_{0}+\omega+1\)
|
\((100)+\omega+2\)
|
\((100)+\omega+1\)
|
\(\varepsilon_{0}+\omega+2\)
|
\((100)+\omega+\omega\)
|
\((100)+\omega\)
\((100)+\omega+1\) \((100)+\omega+2\) |
\(\varepsilon_{0}+\omega+\omega\)
|
\((100)+(002)\)
|
\((100)+\omega\)
\((100)+\omega+1\) \((100)+\omega+2\) |
\(\varepsilon_{0}+\omega^{2}\)
|
\((100)+(00\omega)\)
|
\((100)+(000)\)
\((100)+(001)\) \((100)+(002)\) |
\(\varepsilon_{0}+\omega^{\omega}\)
|
\((100)+(00\omega+1)\)
|
\((100)\)
\((100)+(00\omega)\) \((100)+(00\omega)+(00\omega)\) |
\(\varepsilon_{0}+\omega^{\omega+1}\)
|
\((100)+(00\omega+2)\)
|
\((100)\)
\((100)+(00\omega+1)\) \((100)+(00\omega+1)+(00\omega+1)\) |
\(\varepsilon_{0}+\omega^{\omega+2}\)
|
\((100)+(00\omega+\omega)\)
|
\((100)+(00\omega)\)
\((100)+(00\omega+1)\) \((100)+(00\omega+2)\) |
\(\varepsilon_{0}+\omega^{\omega+\omega}\)
|
\((100)+(00(002))\)
|
\((100)+(000)\)
\((100)+(00\omega)\) \((100)+(00\omega+\omega)\) |
\(\varepsilon_{0}+\omega^{\omega^{2}}\)
|
\((100)+(00(00\omega))\)
|
\((100)+(000)\)
\((100)+(00\omega)\) \((100)+(00\omega+\omega)\) |
\(\varepsilon_{0}+\omega^{\omega^{\omega}}\)
|
\((100)+(00(00(00\omega)))\)
|
\((100)+(00(000))\)
\((100)+(00(00\omega))\) \((100)+(00(00\omega+\omega))\) |
\(\varepsilon_{0}+\omega^{\omega^{\omega^{\omega}}}\)
|
\((100)+(010)\)
|
\((100)+\omega\)
\((100)+(00\omega)\) \((100)+(00(00\omega))\) |
\(\varepsilon_{0}+\varepsilon_{0}\)
|
\((100)+(010)+(010)\)
|
\((100)+(010)+\omega\)
\((100)+(010)+(00\omega)\) \((100)+(010)+(00(00\omega))\) |
\(\varepsilon_{0}+\varepsilon_{0}+\varepsilon_{0}\)
|
\((100)+(00(010)+1)\)
|
\((100)\)
\((100)+(010)\) \((100)+(010)+(010)\) |
\(\omega^{\varepsilon_{0}+1}\)
|
\((100)+(00(010)+2)\)
|
\((100)\)
\((100)+(00(010)+1)\) \((100)+(00(010)+1)+(00(010)+1)\) |
\(\omega^{\varepsilon_{0}+2}\)
|
\((100)+(00(010)+\omega)\)
|
\((100)+(010)\)
\((100)+(00(010)+1)\) \((100)+(00(010)+2)\) |
\(\omega^{\varepsilon_{0}+\omega}\)
|
\((100)+(00(010)+(00\omega))\)
|
\((100)+(00(010)+(000))\)
\((100)+(00(010)+(001))\) \((100)+(00(010)+(002))\) |
\(\omega^{\varepsilon_{0}+\omega^{\omega}}\)
|
\((100)+(00(010)+(00(00\omega)))\)
|
\((100)+(00(010)+(00(000)))\)
\((100)+(00(010)+(00(001)))\) \((100)+(00(010)+(00(002)))\) |
\(\omega^{\varepsilon_{0}+\omega^{\omega^{\omega}}}\)
|
\((100)+(00(010)+(010))\)
|
\((100)+(00(010)+\omega)\)
\((100)+(00(010)+(00\omega))\) \((100)+(00(010)+(00(00\omega)))\) |
\(\omega^{\varepsilon_{0}+\varepsilon_{0}}\)
|
\((100)+(00(00(010)+1))\)
|
\((100)+(000)\)
\((100)+(00(010))\) \((100)+(00(010)+(010))\) |
\(\omega^{\omega^{\varepsilon_{0}+1}}\)
|
\((100)+(011)\)
|
\((100)+(010)+1\)
\((100)+(00(010)+1)\) \((100)+(00(00(010)+1))\) |
\(\varepsilon_{1}\)
|
\((100)+(012)\)
|
\((100)+(011)+1\)
\((100)+(00(011)+1)\) \((100)+(00(00(011)+1))\) |
\(\varepsilon_{2}\)
|
\((100)+(01\omega)\)
|
\((100)+(010)\)
\((100)+(011)\) \((100)+(012)\) |
\(\varepsilon_{\omega}\)
|
\((100)+(01(00\omega))\)
|
\((100)+(01(000))\)
\((100)+(01(001))\) \((100)+(01(002))\) |
\(\varepsilon_{\omega^{\omega}}\)
|
\((100)+(01(00(00\omega)))\)
|
\((100)+(01(00(000)))\)
\((100)+(01(00(001)))\) \((100)+(01(00(002)))\) |
\(\varepsilon_{\omega^{\omega^{\omega}}}\)
|
\((100)+(01(010))\)
|
\((100)+(01\omega)\)
\((100)+(01(00\omega))\) \((100)+(01(00(00\omega)))\) |
\(\varepsilon_{\varepsilon_{0}}\)
|
\((100)+(100)\)
|
\((100)\)
\((100)+(010)\) \((100)+(01(010))\) |
\(\varepsilon_{\cdot_{\cdot_{\cdot_{\varepsilon_{0}}}}}\)
\(= \zeta_0\) |
Up to \(\Gamma_0\)[]
I describe the ordinal types into normal forms for Veblen function. The map \((b,c) \mapsto (0bc)\) plays a role analogous to the map \((\beta,\gamma) \mapsto \varphi_{\beta}(\gamma)\), but \(o\) does not preserve the structure because it does not preserve the addition. For example, \(o((00(100)+1))\) is intended to coincide with \(\varphi_{\omega}(0)\), which is much greater than \(\varphi_{0}(o((100)+1)) = \omega^{\varepsilon_0+1}\).
| expression \(\alpha \in OT\) | modified fundamental sequence | ordinal \(o(\alpha) \in \Omega\) |
|---|---|---|
\((100)+(100)\)
|
\((100)\)
\((100)+(010)\) \((100)+(01(010))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)\)
\(= \zeta_{0}\) |
\((100)+(100)+1\)
|
\((100)+(100)\)
|
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0)\)
\(= \zeta_{0}+1\) |
\((100)+(100)+2\)
|
\((100)+(100)+1\)
|
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0)+\varphi_{0}(0)\)
\(= \zeta_{0}+2\) |
\((100)+(100)+\omega\)
|
\((100)+(100)\)
\((100)+(100)+1\) \((100)+(100)+2\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(\varphi_{0}(0))\)
\(= \zeta_{0}+\omega\) |
\((100)+(100)+(00\omega)\)
|
\((100)+(100)+(000)\)
\((100)+(100)+(001)\) \((100)+(100)+(002)\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(\varphi_{0}(\varphi_{0}(0)))\)
\(= \zeta_{0}+\omega^{\omega}\) |
\((100)+(100)+(010)\)
|
\((100)+(100)+\omega\)
\((100)+(100)+(00\omega)\) \((100)+(100)+(00(00\omega))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(0)\)
\(= \zeta_{0}+\varepsilon_{0}\) |
\((100)+(100)+(010)+(010)\)
|
\((100)+(100)+(010)+\omega\)
\((100)+(100)+(010)+(00\omega)\) \((100)+(100)+(010)+(00(00\omega))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(0)\)
\(= \zeta_{0}+\varepsilon_{0}+\varepsilon_{0}\) |
\((100)+(100)+(00(010)+1)\)
|
\((100)+(100)\)
\((100)+(100)+(010)\) \((100)+(100)+(010)+(010)\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(\varphi_{\varphi_{0}(0)}(0)+\varphi_{0}(0))\)
\(= \zeta_{0}+\omega^{\varepsilon_{0}+1}\) |
\((100)+(100)+(00(00(010)+1))\)
|
\((100)+(100)+(000)\)
\((100)+(100)+(010)\) \((100)+(100)+(00(010)+(010))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(\varphi_{0}(\varphi_{\varphi_{0}(0)}(0)+\varphi_{0}(0)))\)
\(= \zeta_{0}+\omega^{\omega^{\varepsilon_{0}+1}}\) |
\((100)+(100)+(011)\)
|
\((100)+(100)+(010)+1\)
\((100)+(100)+(00(010)+1)\) \((100)+(100)+(00(00(010)+1))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(\varphi_{0}(0))\)
\(= \zeta_{0}+\varepsilon_{1}\) |
\((100)+(100)+(01\omega)\)
|
\((100)+(100)+(010)\)
\((100)+(100)+(011)\) \((100)+(100)+(012)\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(\varphi_{0}(\varphi_{0}(0)))\)
\(= \zeta_{0}+\varepsilon_{\omega}\) |
\((100)+(100)+(01(010))\)
|
\((100)+(100)+(01\omega)\)
\((100)+(100)+(01(00\omega))\) \((100)+(100)+(01(00(00\omega)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)}(0))\)
\(= \zeta_{0}+\varepsilon_{\varepsilon_{0}}\) |
\((100)+(100)+(01(01(010)))\)
|
\((100)+(100)+(01(01\omega))\)
\((100)+(100)+(01(01(00\omega)))\) \((100)+(100)+(01(01(00(00\omega))))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)}(0)))\)
\(= \zeta_{0}+\varepsilon_{\varepsilon_{\varepsilon_{0}}}\) |
\((100)+(100)+(020)\)
|
\((100)+(100)+(010)\)
\((100)+(100)+(01(010)\) \((100)+(100)+(01(01(010)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)\)
\(= \zeta_{0}+\zeta_{0}\) |
\((100)+(100)+(020)+1\)
|
\((100)+(100)+(020)\)
|
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0)\)
\(= \zeta_{0}+\zeta_{0}+1\) |
\((100)+(100)+(020)+(010)\)
|
\((100)+(100)+(020)+\omega\)
\((100)+(100)+(020)+(00\omega)\) \((100)+(100)+(020)+(00(00\omega))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)}(0)\)
\(= \zeta_{0}+\zeta_{0}+\varepsilon_{0}\) |
\((100)+(100)+(020)+(020)\)
|
\((100)+(100)+(020)+(010)\)
\((100)+(100)+(020)+(01(010))\) \((100)+(100)+(020)+(01(01(010)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)\)
\(= \zeta_{0}+\zeta_{0}+\zeta_{0}\) |
\((100)+(100)+(00(020)+1)\)
|
\((100)+(100)\)
\((100)+(100)+(020)\) \((100)+(100)+(020)+(020)\) |
\(\varphi_{0}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0))\)
\(= \omega^{\zeta_{0}+1}\) |
\((100)+(100)+(00(00(020)+1))\)
|
\((100)+(100)+(000)\)
\((100)+(100)+(00(020))\) \((100)+(100)+(00(020)+(020))\) |
\(\varphi_{0}(\varphi_{0}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0)))\)
\(= \omega^{\omega^{\zeta_{0}+1}}\) |
\((100)+(100)+(01(020)+1)\)
|
\((100)+(100)+(020)+1\)
\((100)+(100)+(00(020)+1)\) \((100)+(100)+(00(00(020)+1))\) |
\(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0))\)
\(= \varepsilon_{\zeta_{0}+1}\) |
\((100)+(100)+(01(01(020)+1))\)
|
\((100)+(100)+(01(020)+1)\)
\((100)+(100)+(01(00(020)+1))\) \((100)+(100)+(01(00(00(020)+1)))\) |
\(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)+\varphi_{0}(0)))\)
\(= \varepsilon_{\varepsilon_{\zeta_{0}+1}}\) |
\((100)+(100)+(021)\)
|
\((100)+(100)+(020)+1\)
\((100)+(100)+(01(020)+1)\) \((100)+(100)+(01(01(020)+1))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(0))\)
\(= \zeta_{1}\) |
\((100)+(100)+(01(021)+1)\)
|
\((100)+(100)+(021)+1\)
\((100)+(100)+(00(021)+1)\) \((100)+(100)+(00(00(021)+1))\) |
\(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(0))+\varphi_{0}(0))\)
\(= \varepsilon_{\zeta_{1}+1}\) |
\((100)+(100)+(01(01(021)+1))\)
|
\((100)+(100)+(01(021)+1)\)
\((100)+(100)+(01(00(021)+1))\) \((100)+(100)+(01(00(00(021)+1)))\) |
\(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(0))+\varphi_{0}(0)))\)
\(= \varepsilon_{\varepsilon_{\zeta_{1}+1}}\) |
\((100)+(100)+(022)\)
|
\((100)+(100)+(021)+1\)
\((100)+(100)+(01(021)+1)\) \((100)+(100)+(01(01(021)+1))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(0)+\varphi_{0}(0))\)
\(= \zeta_{2}\) |
\((100)+(100)+(02\omega)\)
|
\((100)+(100)+(020)\)
\((100)+(100)+(021)\) \((100)+(100)+(022)\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(\varphi_{0}(0)))\)
\(= \zeta_{\omega}\) |
\((100)+(100)+(02(010))\)
|
\((100)+(100)+(02\omega)\)
\((100)+(100)+(02(00\omega))\) \((100)+(100)+(02(00(00\omega)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{0}(\varphi_{\varphi_{0}(0)}(0)))\)
\(= \zeta_{\varepsilon_{0}}\) |
\((100)+(100)+(02(020))\)
|
\((100)+(100)+(02(010)+1)\)
\((100)+(100)+(02(01(010)+1))\) \((100)+(100)+(02(01(01(010)+1)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0))\)
\(= \zeta_{\zeta_{0}}\) |
\((100)+(100)+(100)\)
|
\((100)+(100)+(020)\)
\((100)+(100)+(02(020))\) \((100)+(100)+(02(02(020)))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)+\varphi_{0}(0)}(0)\)
\(= \eta_{0}\) |
\((00(100)+1)\)
|
\(0\)
\((100)\) \((100)+(100)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)\)
\(= \varphi_{\omega}(0)\) |
\((00(100)+1)+(0{\omega}0)\)
|
\((00(100)+1)+(000)\)
\((00(100)+1)+(010)\) \((00(100)+1)+(020)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)\)
\(= \varphi_{\omega}(0)+\varphi_{\omega}(0)\) |
\((00(100)+1)+(0{\omega}0)+(0{\omega}0)\)
|
\((00(100)+1)+(0{\omega}0)+(000)\)
\((00(100)+1)+(0{\omega}0)+(010)\) \((00(100)+1)+(0{\omega}0)+(020)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)\)
\(= \varphi_{\omega}(0)+\varphi_{\omega}(0)+\varphi_{\omega}(0)\) |
\((00(100)+1)+(00(0{\omega}0)+1)\)
|
\((00(100)+1)\)
\((00(100)+1)+(0{\omega}0)\) \((00(100)+1)+(0{\omega}0)+(0{\omega}0)\) |
\(\varphi_{0}(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{0}(0))\)
\(= \omega^{\varphi_{\omega}(0)+1}\) |
\((00(100)+1)+(01(0{\omega}0)+1)\)
|
\((00(100)+1)+(0{\omega}0)+1\)
\((00(100)+1)+(00(0{\omega}0)+1)\) \((00(100)+1)+(00(00(0{\omega}0)+1))\) |
\(\varphi_{\varphi_{0}(0)}(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{0}(0))\)
\(= \varepsilon_{\varphi_{\omega}(0)+1}\) |
\((00(100)+1)+(02(0{\omega}0)+1)\)
|
\((00(100)+1)+(0{\omega}0)+1\)
\((00(100)+1)+(01(0{\omega}0)+1)\) \((00(100)+1)+(01(01(0{\omega}0)+1))\) |
\(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)+\varphi_{0}(0))\)
\(= \zeta_{\varphi_{\omega}(0)+1}\) |
\((00(100)+1)+(0{\omega}1)\)
|
\((00(100)+1)+(00(0{\omega}0)+1)\)
\((00(100)+1)+(01(0{\omega}0)+1)\) \((00(100)+1)+(02(0{\omega}0)+1)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{0}(0))\)
\(= \varphi_{\omega}(1)\) |
\((00(100)+1)+(0{\omega}2)\)
|
\((00(100)+1)+(00(0{\omega}1)+1)\)
\((00(100)+1)+(01(0{\omega}1)+1)\) \((00(100)+1)+(02(0{\omega}1)+1)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{0}(0)+\varphi_{0}(0))\)
\(= \varphi_{\omega}(2)\) |
\((00(100)+1)+(0{\omega}\omega)\)
|
\((00(100)+1)+(0{\omega}0)\)
\((00(100)+1)+(0{\omega}1)\) \((00(100)+1)+(0{\omega}2)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{0}(\varphi_{0}(0)))\)
\(= \varphi_{\omega}(\omega)\) |
\((00(100)+1)+(0{\omega}(010))\)
|
\((00(100)+1)+(0{\omega}\omega)\)
\((00(100)+1)+(0{\omega}(00\omega))\) \((00(100)+1)+(0{\omega}(00(00\omega)))\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{\varphi_{0}(0)}(0))\)
\(= \varphi_{\omega}(\varepsilon_{0})\) |
\((00(100)+1)+(0{\omega}(020))\)
|
\((00(100)+1)+(0{\omega}(010))\)
\((00(100)+1)+(0{\omega}(01(010)))\) \((00(100)+1)+(0{\omega}(01(01(010))))\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0))\)
\(= \varphi_{\omega}(\zeta_{0})\) |
\((00(100)+1)+(0{\omega}(0{\omega}0))\)
|
\((00(100)+1)+(0{\omega}(000))\)
\((00(100)+1)+(0{\omega}(010))\) \((00(100)+1)+(0{\omega}(020))\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))}(\varphi_{\varphi_{0}(\varphi_{0}(0))}(0))\)
\(= \varphi_{\omega}(\varphi_{\omega}(0))\) |
\((00(100)+1)+(100)\)
|
\((00(100)+1)+(0{\omega}0)\)
\((00(100)+1)+(0{\omega}(0{\omega}0))\) \((00(100)+1)+(0{\omega}(0{\omega}(0{\omega}0)))\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))+\varphi_{0}(0)}(0)\)
\(= \varphi_{\omega+1}(0)\) |
\((00(100)+1)+(100)+(100)\)
|
\((00(100)+1)+(100)+(0\omega+10)\)
\((00(100)+1)+(100)+(0\omega+1(0\omega+10))\) \((00(100)+1)+(100)+(0\omega+1(0\omega+1(0\omega+10)))\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))+\varphi_{0}(0)+\varphi_{0}(0)}(0)\)
\(= \varphi_{\omega+2}(0)\) |
\((00(100)+1)+(00(100)+1)\)
|
\((00(100)+1)\)
\((00(100)+1)+(100)\) \((00(100)+1)+(100)+(100)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0))+\varphi_{0}(\varphi_{0}(0))}(0)\)
\(= \varphi_{\omega+\omega}(0)\) |
\((00(100)+2)\)
|
\(0\)
\((00(100)+1)\) \((00(100)+1)+(00(100)+1)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(0)+\varphi_{0}(0))}(0)\)
\(= \varphi_{\omega^2}(0)\) |
\((00(100)+\omega)\)
|
\((00(100))\)
\((00(100)+1)\) \((00(100)+2)\) |
\(\varphi_{\varphi_{0}(\varphi_{0}(\varphi_{0}(0)))}(0)\)
\(= \varphi_{\omega^{\omega}}(0)\) |
\((00(100)+(010))\)
|
\((00(100)+\omega)\)
\((00(100)+(00\omega))\) \((00(100)+(00(00\omega)))\) |
\(\varphi_{\varphi_{\varphi_{0}(0)}(0)}(0)\)
\(= \varphi_{\varepsilon_{0}}(0)\) |
\((00(100)+(020))\)
|
\((00(100)+(010))\)
\((00(100)+(01(010)))\) \((00(100)+(01(01(010))))\) |
\(\varphi_{\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)}(0)\)
\(= \varphi_{\zeta_{0}}(0)\) |
\((00(100)+(0{\omega}0))\)
|
\((00(100)+(000))\)
\((00(100)+(010))\) \((00(100)+(020))\) |
\(\varphi_{\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)}(0)\)
\(= \varphi_{\varphi_{\omega}(0)}(0)\) |
\((00(100)+(0(010)0))\)
|
\((00(100)+(0{\omega}0))\)
\((00(100)+(0(00\omega)0))\) \((00(100)+(0(00(00\omega))0))\) |
\(\varphi_{\varphi_{\varphi_{\varphi_{0}(0)}(0)}(0)}(0)\)
\(= \varphi_{\varphi_{\varepsilon_{0}}(0)}(0)\) |
\((00(100)+(0(020)0))\)
|
\((00(100)+(0(010)0))\)
\((00(100)+(0(01(010))0))\) \((00(100)+(0(01(01(010)))0))\) |
\(\varphi_{\varphi_{\varphi_{\varphi_{0}(0)+\varphi_{0}(0)}(0)}(0)}(0)\)
\(= \varphi_{\varphi_{\zeta_{0}}(0)}(0)\) |
\((00(100)+(0(0{\omega}0)0))\)
|
\((00(100)+(0(000)0))\)
\((00(100)+(0(010)0))\) \((00(100)+(0(020)0))\) |
\(\varphi_{\varphi_{\varphi_{\varphi_{0}(\varphi_{0}(0))}(0)}(0)}(0)\)
\(= \varphi_{\varphi_{\varphi_{\omega}(0)}(0)}(0)\) |
\((00(100)+(100))\)
|
\((00(100)+1)\)
\((00(100)+(010))\) \((00(100)+(0(010)0))\) |
\(\varphi_{\varphi_{\cdot_{\cdot_{\cdot_{\varphi_{0}(0)}\cdot}\cdot}\cdot}(0)}(0)\)
\(= \Gamma_0\) |
Up to BHO[]
I describe the ordinal types into normal forms for Buchholz's function restericted to expressions consisting of \(0\), \(+\), \(\psi_0\), and \(\psi_1\).
| expression \(\alpha \in OT\) | modified fundamental sequence | ordinal \(o(\alpha) \in \Omega\) |
|---|---|---|
\((00(100)+(100))\)
|
\((00(100)+1)\)
\((00(100)+(00(100)+1))\) \((00(100)+(00(100)+(00(100)+1)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega})\) \(= \Gamma_0\) |
\((00(100)+(100))+(0(100)0)\)
|
\((00(100)+(100))+1\)
\((00(100)+(100))+(010)\) \((00(100)+(100))+(0(010)0)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega})+\psi_0(\Omega^{\Omega})\) |
\((00(100)+(100))+(0(100)0)+(0(100)0)\)
|
\((00(100)+(100))+(0(100)0)+1\)
\((00(100)+(100))+(0(100)0)+(010)\) \((00(100)+(100))+(0(100)0)+(0(010)0)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega})+\psi_0(\Omega^{\Omega})+\psi_0(\Omega^{\Omega})\) |
\((00(100)+(100))+(00(0(100)0)+1)\)
|
\((00(100)+(100))\)
\((00(100)+(100))+(0(100)0)\) \((00(100)+(100))+(0(100)0)+(0(100)0)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_0(0))\)
\(= \psi_0(\Omega^{\Omega}+1)\) |
\((00(100)+(100))+(01(0(100)0)+1)\)
|
\((00(100)+(100))+(0(100)0)+1\)
\((00(100)+(100))+(00(0(100)0)+1)\) \((00(100)+(100))+(00(00(0(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0))\)
\(= \psi_0(\Omega^{\Omega}+\Omega)\) |
\((00(100)+(100))+(02(0(100)0)+1)\)
|
\((00(100)+(100))+(0(100)0)+1\)
\((00(100)+(100))+(01(0(100)0)+1)\) \((00(100)+(100))+(01(01(0(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{2})\) |
\((00(100)+(100))+(0\omega(0(100)0)+1)\)
|
\((00(100)+(100))+(00(0(100)0)+1)\)
\((00(100)+(100))+(01(0(100)0)+1)\) \((00(100)+(100))+(02(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\omega})\) |
\((00(100)+(100))+(0\omega+\omega(0(100)0)+1)\)
|
\((00(100)+(100))+(0\omega(0(100)0)+1)\)
\((00(100)+(100))+(0\omega+1(0(100)0)+1)\) \((00(100)+(100))+(0\omega+2(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0)+\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\omega^{2}})\) |
\((00(100)+(100))+(0(00\omega)(0(100)0)+1)\)
|
\((00(100)+(100))+(00(0(100)0)+1)\)
\((00(100)+(100))+(0\omega(0(100)0)+1)\) \((00(100)+(100))+(0\omega+\omega(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_0(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\omega^{\omega}})\) |
\((00(100)+(100))+(0(010)(0(100)0)+1)\)
|
\((00(100)+(100))+(00(0(100)0)+1)\)
\((00(100)+(100))+(01(0(100)0)+1)\) \((00(100)+(100))+(0\omega(0(100)0)+1)\) \((00(100)+(100))+(0(00\omega)(0(100)0)+1)\) \((00(100)+(100))+(0(00(00\omega))(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega)})\) |
\((00(100)+(100))+(0(020)(0(100)0)+1)\)
|
\((00(100)+(100))+(00(0(100)0)+1)\)
\((00(100)+(100))+(0(010)(0(100)0)+1)\) \((00(100)+(100))+(0(01(010))(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{2})})\) |
\((00(100)+(100))+(0(0{\omega}0)(0(100)0)+1)\)
|
\((00(100)+(100))+(0(000)(0(100)0)+1)\)
\((00(100)+(100))+(0(010)(0(100)0)+1)\) \((00(100)+(100))+(0(020)(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\omega})})\) |
\((00(100)+(100))+(0(100)1)\)
|
\((00(100)+(100))+(01(0(100)0)+1)\)
\((00(100)+(100))+(0(010)(0(100)0)+1)\) \((00(100)+(100))+(0(0(010)0)(0(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})})\) |
\((00(100)+(100))+(0(100)2)\)
|
\((00(100)+(100))+(01(0(100)1)+1)\)
\((00(100)+(100))+(0(010)(0(100)1)+1)\) \((00(100)+(100))+(0(0(010)0)(0(100)1)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times 2)\) \(= \varphi_{\Gamma_0}(1)\) |
\((00(100)+(100))+(0(100)\omega)\)
|
\((00(100)+(100))+(0(100)0)\)
\((00(100)+(100))+(0(100)1)\) \((00(100)+(100))+(0(100)2)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \omega)\) \(= \varphi_{\Gamma_0}(\omega)\) |
\((00(100)+(100))+(0(100)\omega+\omega)\)
|
\((00(100)+(100))+(0(100)\omega)\)
\((00(100)+(100))+(0(100)\omega+1)\) \((00(100)+(100))+(0(100)\omega+2)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(0))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\omega+\omega))\) \(= \varphi_{\Gamma_0}(\omega+\omega)\) |
\((00(100)+(100))+(0(100)(002))\)
|
\((00(100)+(100))+(0(100)0)\)
\((00(100)+(100))+(0(100)\omega)\) \((00(100)+(100))+(0(100)\omega+\omega)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(0)+\psi_0(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \omega^{2})\) \(= \varphi_{\Gamma_0}(\omega^{2})\) |
\((00(100)+(100))+(0(100)(00\omega))\)
|
\((00(100)+(100))+(0(100)(000))\)
\((00(100)+(100))+(0(100)(001))\) \((00(100)+(100))+(0(100)(002))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\psi_0(\Omega^{2})})} \times \omega^{\omega})\) \(= \varphi_{\Gamma_0}(\omega^{\omega})\) |
\((00(100)+(100))+(0(100)(010))\)
|
\((00(100)+(100))+(0(100)0)\)
\((00(100)+(100))+(0(100)1)\) \((00(100)+(100))+(0(100)\omega)\) \((00(100)+(100))+(0(100)(00\omega))\) \((00(100)+(100))+(0(100)(00(00\omega)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega))\) \(= \varphi_{\Gamma_0}(\varepsilon_0)\) |
\((00(100)+(100))+(0(100)(020))\)
|
\((00(100)+(100))+(0(100)0)\)
\((00(100)+(100))+(0(100)(010))\) \((00(100)+(100))+(0(100)(01(010)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega^{2}))\) \(= \varphi_{\Gamma_0}(\zeta_0)\) |
\((00(100)+(100))+(0(100)(0{\omega}0))\)
|
\((00(100)+(100))+(0(100)(000))\)
\((00(100)+(100))+(0(100)(010))\) \((00(100)+(100))+(0(100)(020))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(\psi_0(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega^{\omega}))\) \(= \varphi_{\Gamma_0}(\varphi_{\omega}(0))\) |
\((00(100)+(100))+(0(100)(0(010)0))\)
|
\((00(100)+(100))+(0(100)(000))\)
\((00(100)+(100))+(0(100)(010))\) \((00(100)+(100))+(0(100)(0{\omega}0))\) \((00(100)+(100))+(0(100)(0(00\omega)0))\) \((00(100)+(100))+(0(100)(0(00(00\omega))0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(\psi_0(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega^{\psi_0(\Omega)}))\) \(= \varphi_{\Gamma_0}(\varphi_{\varepsilon_0}(0))\) |
\((00(100)+(100))+(0(100)(0(0{\omega}0)0))\)
|
\((00(100)+(100))+(0(100)(0{000}0))\)
\((00(100)+(100))+(0(100)(0(010)0))\) \((00(100)+(100))+(0(100)(0(020)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_0(0)))))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega^{\psi_0(\Omega^{\omega})}))\) \(= \varphi_{\Gamma_0}(\varphi_{\varphi_{\omega}}(0))\) |
\((00(100)+(100))+(0(100)(0(100)0))\)
|
\((00(100)+(100))+(0(100)0)\)
\((00(100)+(100))+(0(100)1)\) \((00(100)+(100))+(0(100)(010))\) \((00(100)+(100))+(0(100)(0(010)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \psi_0(\Omega^{\Omega}))\) \(= \varphi_{\Gamma_0}(\varphi_{\Gamma_0}(0))\) |
\((00(100)+(100))+(100)\)
|
\((00(100)+(100))\)
\((00(100)+(100))+(0(100)0)\) \((00(100)+(100))+(0(100)(0(100)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega)\) \(= \varphi_{\Gamma_0+1}(0)\) |
\((00(100)+(100))+(100)+(0(100)+10)\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(100)+(0(100)0)\) \((00(100)+(100))+(100)+(0(100)(0(100)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))+\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega) \times 2\) \(= \varphi_{\Gamma_0+1}(0) \times 2\) |
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(100)+(0(100)+10)\) \((00(100)+(100))+(100)+(0(100)+10)+(0(100)+10)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_0(0))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega) \times \omega\) \(= \varphi_{\Gamma_0+1}(0) \times \omega\) |
\((00(100)+(100))+(100)+(01(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(0(100)+10)+1\)
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\) \((00(100)+(100))+(100)+(00(00(0(100)+10)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(0))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega + \Omega)\) \(= \varepsilon_{\varphi_{\Gamma_0+1}(0)+1}\) |
\((00(100)+(100))+(100)+(02(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(0(100)+10)+1\)
\((00(100)+(100))+(100)+(01(0(100)+10)+1)\) \((00(100)+(100))+(100)+(01(01(0(100)+10)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega + \Omega^{2})\) \(= \zeta_{\varphi_{\Gamma_0+1}(0)+1}\) |
\((00(100)+(100))+(100)+(0\omega(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\)
\((00(100)+(100))+(100)+(01(0(100)+10)+1)\) \((00(100)+(100))+(100)+(02(0(100)+10)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega + \Omega^{\omega})\) \(= \varphi_{\omega}(\varphi_{\Gamma_0+1}(0)+1)\) |
\((00(100)+(100))+(100)+(0(010)(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\)
\((00(100)+(100))+(100)+(01(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0\omega(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0(00\omega)(0(100)+10)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(\psi_0(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega + \Omega^{\psi_0(\Omega)})\) \(= \varphi_{\varepsilon}(\varphi_{\Gamma_0+1}(0)+1)\) |
\((00(100)+(100))+(100)+(0(020)(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\)
\((00(100)+(100))+(100)+(0(010)(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0(01(010))(0(100)+10)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega + \Omega^{\psi_0(\Omega^{2})})\) \(= \varphi_{\zeta_0}(\varphi_{\Gamma_0+1}(0)+1)\) |
\((00(100)+(100))+(100)+(0(100)(0(100)+10)+1)\)
|
\((00(100)+(100))+(100)+(00(0(100)+10)+1)\)
\((00(100)+(100))+(100)+(01(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0(010)(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0(0(010)0)(0(100)+10)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega+1))\) \(= \varphi_{\Gamma_0}(\varphi_{\Gamma_0+1}(0)+1)\) |
\((00(100)+(100))+(100)+(0(100)+11)\)
|
\((00(100)+(100))+(100)+(0(100)+10)+1\)
\((00(100)+(100))+(100)+(0(100)(0(100)+10)+1)\) \((00(100)+(100))+(100)+(0(100)(0(100)(0(100)+10)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times 2)\) \(= \varphi_{\Gamma_0+1}(1)\) |
\((00(100)+(100))+(100)+(0(100)+1\omega)\)
|
\((00(100)+(100))+(100)+(0(100)+10)\)
\((00(100)+(100))+(100)+(0(100)+11)\) \((00(100)+(100))+(100)+(0(100)+12)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \omega)\) \(= \varphi_{\Gamma_0+1}(\omega)\) |
\((00(100)+(100))+(100)+(0(100)+1(010))\)
|
\((00(100)+(100))+(100)+(0(100)+10)\)
\((00(100)+(100))+(100)+(0(100)+11)\) \((00(100)+(100))+(100)+(0(100)+1\omega)\) \((00(100)+(100))+(100)+(0(100)+1(00\omega))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \psi_0(\Omega))\) \(= \varphi_{\Gamma_0+1}(\varepsilon_0)\) |
\((00(100)+(100))+(100)+(0(100)+1(020))\)
|
\((00(100)+(100))+(100)+(0(100)+10)\)
\((00(100)+(100))+(100)+(0(100)+1(010))\) \((00(100)+(100))+(100)+(0(100)+1(01(010)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(\psi_1(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \psi_0(\Omega^{2}))\) \(= \varphi_{\Gamma_0+1}(\zeta_0)\) |
\((00(100)+(100))+(100)+(0(100)+1(0{\omega}0))\)
|
\((00(100)+(100))+(100)+(0(100)+1(000))\)
\((00(100)+(100))+(100)+(0(100)+1(010))\) \((00(100)+(100))+(100)+(0(100)+1(020))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(\psi_1(\psi_1(\psi_0(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \psi_0(\Omega^{\omega}))\) \(= \varphi_{\Gamma_0+1}(\varphi_{\omega}(0))\) |
\((00(100)+(100))+(100)+(0(100)+1(0(100)0))\)
|
\((00(100)+(100))+(100)+(0(100)+1(000))\)
\((00(100)+(100))+(100)+(0(100)+1(010))\) \((00(100)+(100))+(100)+(0(100)+1(0(010)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(\psi_1(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \psi_0(\Omega^{\Omega}))\) \(= \varphi_{\Gamma_0+1}(\Gamma_0)\) |
\((00(100)+(100))+(100)+(0(100)+1(0(100)+10))\)
|
\((00(100)+(100))+(100)+(0(100)+10)\)
\((00(100)+(100))+(100)+(0(100)+1(0(100)0))\) \((00(100)+(100))+(100)+(0(100)+1(0(100)(0(100)0)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times (\Omega \times \psi_0(\Omega^{\Omega}))\) \(= \varphi_{\Gamma_0+1}(\varphi_{\Gamma_0+1}(0))\) |
\((00(100)+(100))+(100)+(100)\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(100)+(0(100)+10)\) \((00(100)+(100))+(100)+(0(100)+1(0(100)+10))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{2})\) \(= \varphi_{\Gamma_0+2}(0)\) |
\((00(100)+(100))+(00(100)+1)\)
|
\((00(100)+(100))\)
\((00(100)+(100))+(100)\) \((00(100)+(100))+(100)+(100)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{\omega})\) \(= \varphi_{\Gamma_0+\omega}(0)\) |
\((00(100)+(100))+(00(100)+(010))\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+1)\) \((00(100)+(100))+(00(100)+\omega)\) \((00(100)+(100))+(00(100)+(00\omega))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{\psi_0(\Omega)})\) \(= \varphi_{\Gamma_0+\varepsilon_0}(0)\) |
\((00(100)+(100))+(00(100)+(020))\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(010))\) \((00(100)+(100))+(00(100)+(01(010)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{\psi_0(\Omega^{2})})\) \(= \varphi_{\Gamma_0+\zeta_0}(0)\) |
\((00(100)+(100))+(00(100)+(0{\omega}0))\)
|
\((00(100)+(100))+(00(100)+(000))\)
\((00(100)+(100))+(00(100)+(010))\) \((00(100)+(100))+(00(100)+(020))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{\psi_0(\Omega^{\omega})})\) \(= \varphi_{\Gamma_0+\varphi_{\omega}(0)}(0)\) |
\((00(100)+(100))+(00(100)+(0(100)0))\)
|
\((00(100)+(100))+(00(100)+(000))\)
\((00(100)+(100))+(00(100)+(010))\) \((00(100)+(100))+(00(100)+(0(010)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega}) \times 2})\) \(= \varphi_{\Gamma_0+\Gamma_0}(0)\) |
\((00(100)+(100))+(00(100)+(00(0(100)0)+1))\)
|
\((00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(0(100)0))\) \((00(100)+(100))+(00(100)+(0(100)0)+(0(100)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega}) \times \omega})\) \(= \varphi_{\Gamma_0 \times \omega}(0)\) |
\((00(100)+(100))+(00(100)+(0(100)+10))\)
|
\((00(100)+(100))+(00(100))\)
\((00(100)+(100))+(00(100)+(0(100)0))\) \((00(100)+(100))+(00(100)+(0(100)(0(100)0)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega}+\Omega^{\psi_0(\Omega^{\Omega})} \times \Omega^{\psi_0(\Omega^{\Omega}+\Omega)})\) \(= \varphi_{\varphi_{\Gamma_0+1}(0)}(0)\) |
\((00(100)+(100))+(00(100)+(100))\)
|
\((00(100)+(100))+(00(100)+(0(100)0))\)
\((00(100)+(100))+(00(100)+(0(100)+(0(100)0)0))\) \((00(100)+(100))+(00(100)+(0(100)+(0(100)+(0(100)0)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 2)\) \(= \Gamma_1\) |
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)\)
|
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)0))\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)0)0))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)+(0(100)0)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 2) \times 2\) \(= \Gamma_1 \times 2\) |
\((00(100)+(100))+(00(100)+(100))+(00(0(100)+(100)0)+1)\)
|
\((00(100)+(100))+(00(100)+(100))\)
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)\) \((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)+(0(100)+(100)0)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_0(0))\)
\(= \psi_0(\Omega^{\Omega} \times 2) \times \omega\) \(= \Gamma_1 \times \omega\) |
\((00(100)+(100))+(00(100)+(100))+(01(0(100)+(100)0)+1)\)
|
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)+1\)
\((00(100)+(100))+(00(100)+(100))+(00(0(100)+(100)0)+1)\) \((00(100)+(100))+(00(100)+(100))+(00(00(0(100)+(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(0))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega)\) \(= \varepsilon_{\Gamma_1+1}\) |
\((00(100)+(100))+(00(100)+(100))+(02(0(100)+(100)0)+1)\)
|
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)+1\)
\((00(100)+(100))+(00(100)+(100))+(01(0(100)+(100)0)+1)\) \((00(100)+(100))+(00(100)+(100))+(01(01(0(100)+(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{2})\) \(= \zeta_{\Gamma_1+1}\) |
\((00(100)+(100))+(00(100)+(100))+(0\omega(0(100)+(100)0)+1)\)
|
\((00(100)+(100))+(00(100)+(100))+(00(0(100)+(100)0)+1)\)
\((00(100)+(100))+(00(100)+(100))+(01(0(100)+(100)0)+1)\) \((00(100)+(100))+(00(100)+(100))+(02(0(100)+(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\omega})\) \(= \varphi_{\omega}(\Gamma_1+1)\) |
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)(0(100)+(100)0))\)
|
\((00(100)+(100))+(00(100)+(100))+(0(100)(0(100)+(100)0)+1)\)
\((00(100)+(100))+(00(100)+(100))+(0(100)+(0(100)0)(0(100)+(100)0)+1)\) \((00(100)+(100))+(00(100)+(100))+(0(100)+(0(100)+(0(100)0)0)(0(100)+(100)0)+1)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))))
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2)})\) \(= \varphi_{\Gamma_1}(\Gamma_1)\) |
\((00(100)+(100))+(00(100)+(100))+(100)\)
|
\((00(100)+(100))+(00(100)+(100))\)
\((00(100)+(100))+(00(100)+(100))+(0(100)+(100)0)\) \((00(100)+(100))+(00(100)+(100))+(0(100)+(100)(0(100)+(100)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2)+1})\) \(= \varphi_{\Gamma_1+1}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(100)+(100)\)
|
\((00(100)+(100))+(00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(100))+(100)+(0(100)+(100)+10)\) \((00(100)+(100))+(00(100)+(100))+(100)+(0(100)+(100)+1(0(100)+(100)+10))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2)+2})\) \(= \varphi_{\Gamma_1+2}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+1)\)
|
\((00(100)+(100))+(00(100)+(100))\)
\((00(100)+(100))+(00(100)+(100))+(100)\) \((00(100)+(100))+(00(100)+(100))+(100)+(100)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2)+\omega})\) \(= \varphi_{\Gamma_1+\omega}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0))\)
|
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)0))\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)0)0))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)+(0(100)0)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2) \times 2})\) \(= \varphi_{\Gamma_1+\Gamma_1}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(00(0(100)+(100)0)+1))\)
|
\((00(100)+(100))+(00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0)+(0(100)+(100)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))+\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2) \times \omega})\) \(= \varphi_{\Gamma_1 \times \omega}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(01(0(100)+(100)0)+1))\)
|
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0)+1)\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(00(0(100)+(100)0)+1))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(00(00(0(100)+(100)0)+1)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2+\Omega)})\) \(= \varphi_{\varepsilon_{\Gamma_1+1}}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0\omega(0(100)+(100)0)+1))\)
|
\((00(100)+(100))+(00(100)+(100))+(00(100)+(00(0(100)+(100)0)+1))\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(01(0(100)+(100)0)+1))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(02(0(100)+(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2+\Omega^{\omega})})\) \(= \varphi_{\varphi_{\omega}(\Gamma_1+1)}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)(0(100)+(100)0)))\)
|
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)(0(100)+(100)0)+1))\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)0)(0(100)+(100)0)+1))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(0(100)+(0(100)0)0)(0(100)+(100)0)+1))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2+\Omega^{\psi_0(\Omega^{\Omega} \times 2)})})\) \(= \varphi_{\varphi_{\Gamma1}(1)}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)+10))\)
|
\((00(100)+(100))+(00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)(0(100)+(100)0)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0)))))))))\)
\(= \psi_0(\Omega^{\Omega} \times 2 + \Omega^{\psi_0(\Omega^{\Omega} \times 2+\Omega^{\psi_0(\Omega^{\Omega} \times 2)+1})})\) \(= \varphi_{\varphi_{\Gamma1+1}(0)}(0)\) |
\((00(100)+(100))+(00(100)+(100))+(00(100)+(100))\)
|
\((00(100)+(100))+(00(100)+(100))+(100)\)
\((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)0))\) \((00(100)+(100))+(00(100)+(100))+(00(100)+(0(100)+(100)+(0(100)+(100)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega} \times 3)\) \(= \Gamma_2\) |
\((00(100)+(100)+1)\)
|
\(0\)
\((00(100)+(100))\) \((00(100)+(100))+(00(100)+(100))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega^{\Omega} \times \omega)\) \(= \Gamma_{\omega}\) |
\((00(100)+(100)+\omega)\)
|
\((00(100)+(100))\)
\((00(100)+(100)+1)\) \((00(100)+(100)+2)\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega} \times \omega^{\omega})\) \(= \Gamma_{\omega^{\omega}}\) |
\((00(100)+(100)+(0(100)+(100)0))\)
|
\((00(100)+(100)+(0(100)0))\)
\((00(100)+(100)+(0(100)+(0(100)0)0))\) \((00(100)+(100)+(0(100)+(0(100)+(0(100)0)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(\psi_1(\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega^{\Omega} \times \psi_0(\Omega^{\Omega} \times 2))\) \(= \Gamma_{\Gamma_1}\) |
\((00(100)+(100)+(100))\)
|
\((00(100)+(100)+(0(100)+(100)0))\)
\((00(100)+(100)+(0(100)+(100)+(0(100)+(100)0)0))\) \((00(100)+(100)+(0(100)+(100)+(0(100)+(100)+(0(100)+(100)0)0)0))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0)))\)
\(= \psi_0(\Omega^{\Omega+1})\) \(= \varphi(1,1,0)\) |
\((00(00(100)+1))\)
|
\((000)\)
\((100)\) \((00(100)+(100))\) \((00(100)+(100)+(100))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega+\omega})\) \(= \varphi(1,\omega,0)\) |
\((00(00(100)+(100)))\)
|
\((00(00(100)+(0(00(100)+1)0)))\)
\((00(00(100)+(0(00(100)+(0(00(100)+1)0))0)))\) \((00(00(100)+(0(00(100)+(0(00(100)+(0(00(100)+1)0))0))0)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega \times 2})\) \(= \varphi(2,0,0)\) |
\((00(00(00(100)+1)))\)
|
\(\omega\)
\((100)\) \((00(00(100)+(100)))\) \((00(00(100)+(100)+(100)))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_0(0))))\)
\(= \psi_0(\Omega^{\Omega \times \omega})\) \(= \varphi(\omega,0,0)\) |
\((00(00(00(100)+(100))))\)
|
\((100)\)
\((00(00(00(100)+(0(100)0))))\) \((00(00(00(100)+(0(00(00(00(100)+(0(100)0))))0))))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_1(0))))\)
\(= \psi_0(\Omega^{\Omega^{2}})\) \(= \varphi(1,0,0,0)\) |
\((00(00(00(00(100)+1))))\)
|
\((00\omega))\)
\((100)\) \((00(00(00(100)+(100))))\) \(00(00(00(100)+(100)+(100))))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega^{\Omega^{\omega}})\) \(= \textrm{SVO}\) |
\((00(00(00(00(100)+(100)))))\)
|
\((00(00(00(00(100)+(0(100)0)))))\)
\((00(00(00(00(100)+(0(00(00(00(00(100)+(0(100)0)))))0)))))\) \((00(00(00(00(100)+(0(00(00(00(00(100)+(0(00(00(00(00(100)+(0(100)0)))))0)))))0)))))\) |
\(\psi_0(\psi_1(\psi_1(\psi_1(\psi_1(0)))))\)
\(= \psi_0(\Omega^{\Omega^{\Omega}})\) \(= \textrm{LVO}\) |
\((01(100)+1)\)
|
\((100)+1\)
\((00(100)+1)\) \((00(00(100)+1))\) |
\(\psi_0(\psi_1(\cdots \psi_1(0)\cdots))\)
\(= \psi_0(\varepsilon_{\Omega+1})\) \(= \psi_0(\Omega_2)\) \(= \textrm{BHO}\) |
Up to \(\psi_0(\Omega_3)\)[]
I describe the ordinal types into normal forms for Buchholz's function restericted to expressions consisting of \(0\), \(+\), \(\psi_0\), \(\psi_1\), and \(\psi_2\). I recall that this is not an analysis, but a table of expectation.
| expression \(\alpha \in OT\) | modified fundamental sequence | ordinal \(o(\alpha) \in \Omega\) |
|---|---|---|
\((01(100)+1)\)
|
\((100)+1\)
\((00(100)+1)\) \((00(00(100)+1))\) |
\(\psi_0(\psi_2(0))\)
\(= \psi_0(\Omega_2)\) \(= \psi_0(\varepsilon_{\Omega+1})\) \(= \textrm{BHO}\) |
\((01(100)+1)+(0(01(100)+1)0)\)
|
\((01(100)+1)+(0(100)+10)\)
\((01(100)+1)+(0(00(100)+1)0)\) \((01(100)+1)+(0(00(00(100)+1))0)\) |
\(\psi_0(\psi_2(0))+\psi_0(\psi_2(0))\)
\(= \psi_0(\Omega_2) \times 2\) |
\((01(100)+1)+(00(0(01(100)+1)0)+1)\)
|
\((01(100)+1)\)
\((01(100)+1)+(0(01(100)+1)0)\) \((01(100)+1)+(0(01(100)+1)0)+(0(01(100)+1)0)\) |
\(\psi_0(\psi_2(0)+\psi_0(0))\)
\(= \psi_0(\Omega_2) \times \omega\) |
\((01(100)+1)+(01(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(0(01(100)+1)0)+1\)
\((01(100)+1)+(00(0(01(100)+1)0)+1)\) \((01(100)+1)+(00(00(0(01(100)+1)0)+1))\) |
\(\psi_0(\psi_2(0)+\psi_1(0))\)
\(= \psi_0(\Omega_2+\Omega)\) |
\((01(100)+1)+(00(01(0(01(100)+1)0)+1)+1)\)
|
\((01(100)+1)\)
\((01(100)+1)+(01(0(01(100)+1)0)+1)\) \((01(100)+1)+(01(0(01(100)+1)0)+1)+(01(0(01(100)+1)0)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_0(0)))\)
\(= \psi_0(\Omega_2+\Omega \times \omega)\) |
\((01(100)+1)+(02(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(0(01(100)+1)0)+1\)
\((01(100)+1)+(01(0(01(100)+1)0)+1)\) \((01(100)+1)+(01(01(0(01(100)+1)0)+1))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(0)))\)
\(= \psi_0(\Omega_2+\Omega^{2})\) |
\((01(100)+1)+(0\omega(0(01(100)+1)0)+1)\)
|
\((01(100)+1)\)
\((01(100)+1)+(01(0(01(100)+1)0)+2)\) \((01(100)+1)+(01(0(01(100)+1)0)+2)+(01(0(01(100)+1)0)+2)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\omega})\) |
\((01(100)+1)+(0(100)(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(0(000)(0(01(100)+1)0)+1)\)
\((01(100)+1)+(0(010)(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(0(010)0)(0(01(100)+1)0)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega^{\Omega})})\) |
\((01(100)+1)+(0(100)+1(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(0(01(100)+1)0)+1\)
\((01(100)+1)+(0(100)(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(100)(0(100)(0(01(100)+1)0)+1))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega^{\Omega+1})})\) |
\((01(100)+1)+(0(00(100)+1)(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(00(0(01(100)+1)0)+1)\)
\((01(100)+1)+(0(100)(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(100)+(100)(0(01(100)+1)0)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_0(0)))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega^{\Omega \times \omega})})\) |
\((01(100)+1)+(0(00(00(100)+1))(0(01(100)+1)0)+1)\)
|
\((01(100)+1)+(0(000)(00(0(01(100)+1)0)+1))\)
\((01(100)+1)+(0(100)(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(00(100)+(100))(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(00(100)+(100)+(100))(0(01(100)+1)0)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega^{\Omega^{\omega}})})\) |
\((01(100)+1)+(0(01(100)+1)1)\)
|
\((01(100)+1)+(0(01(100)+1)0)+1\)
\((01(100)+1)+(0(00(100)+1)(0(01(100)+1)0)+1)\) \((01(100)+1)+(0(00(00(100)+1))(0(01(100)+1)0)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)})\) |
\((01(100)+1)+(0(01(100)+1)2)\)
|
\((01(100)+1)+(0(01(100)+1)1)+1\)
\((01(100)+1)+(0(00(100)+1)(0(01(100)+1)1)+1)\) \((01(100)+1)+(0(00(00(100)+1))(0(01(100)+1)1)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0))))+\psi_1(\psi_1(\psi_0(\psi_2(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)} \times 2)\) |
\((01(100)+1)+(0(01(100)+1)\omega)\)
|
\((01(100)+1)+(0(01(100)+1)0)\)
\((01(100)+1)+(0(01(100)+1)1)\) \((01(100)+1)+(0(01(100)+1)2)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_0(0)))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)} \times \omega)\) |
\((01(100)+1)+(0(01(100)+1)(0(01(100)+1)0))\)
|
\((01(100)+1)+(0(01(100)+1)(0(100)+10))\)
\((01(100)+1)+(0(01(100)+1)(0(00(100)+1)0))\) \((01(100)+1)+(0(01(100)+1)(0(00(00(100)+1))0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_0(\psi_2(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)} \times \psi_0(\psi_2(0))\) |
\((01(100)+1)+(100)\)
|
\((01(100)+1)\)
\((01(100)+1)+(0(01(100)+1)0)\) \((01(100)+1)+(0(01(100)+1)(0(01(100)+1)0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_1(0)))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)+1}\) |
\((01(100)+1)+(100)+(100)\)
|
\((01(100)+1)+(100)\)
\((01(100)+1)+(100)+(0(01(100)+1)+10)\) \((01(100)+1)+(100)+(0(01(100)+1)+1(0(01(100)+1)+10))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_1(0)+\psi_1(0)))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)+2}\) |
\((01(100)+1)+(00(100)+1)\)
|
\((01(100)+1)\)
\((01(100)+1)+(100)\) \((01(100)+1)+(100)+(100)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)+\omega}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\)
|
\((01(100)+1)+(00(100)+(0(100)+10))\)
\((01(100)+1)+(00(100)+(0(00(100)+1)0))\) \((01(100)+1)+(00(100)+(0(00(00(100)+1))0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)))+\psi_1(\psi_0(\psi_2(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2) \times 2}\) |
\((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+1))\)
|
\((01(100)+1)+(100)\)
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\) \((01(100)+1)+(00(100)+(0(01(100)+1)0)+(0(01(100)+1)0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0))+\psi_0(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2) \times \omega}\) |
\((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+(0(01(100)+1)0)))\)
|
\((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+(0(100)+10)))\)
\((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+(0(00(100)+1)0)))\) \((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+(0(00(00(100)+1))0)))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0))+\psi_0(\psi_2(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2) \times \psi_0(\Omega_2)}\) |
\((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+1)))\)
|
\((01(100)+1)+(00(100)+(000))\)
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\) \((01(100)+1)+(00(100)+(0(01(100)+1)0)+(0(01(100)+1)0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_0(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)^{\omega}}\) |
\((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+(0(01(100)+1)0))))\)
|
\((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+(0(100)+10))))\)
\((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+(0(00(100)+1)0))))\) \((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+(0(00(00(100)+1))0))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_0(\psi_2(0))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)^{\psi_0(\Omega_2)}}\) |
\((01(100)+1)+(00(100)+(00(00(00(0(01(100)+1)0)+1))))\)
|
\((01(100)+1)+(00(100)+\omega)\)
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\) \((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+(0(01(100)+1)0))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_0(\psi_2(0)+\psi_0(0))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2)^{\psi_0(\Omega_2)^{\omega}}}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)1))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)0)+1)\)
\((01(100)+1)+(00(100)+(00(0(01(100)+1)0)+1)))\) \((01(100)+1)+(00(100)+(00(00(0(01(100)+1)0)+1))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega)}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)2))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)1)+1)\)
\((01(100)+1)+(00(100)+(00(0(01(100)+1)1)+1)))\) \((01(100)+1)+(00(100)+(00(00(0(01(100)+1)1)+1))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(0)+\psi_1(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega \times 2)}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)\omega))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\)
\((01(100)+1)+(00(100)+(0(01(100)+1)1))\) \((01(100)+1)+(00(100)+(0(01(100)+1)2))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(\psi_0(0))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega \times \omega)}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)(0(01(100)+1)0)))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)(0(100)+10)))\)
\((01(100)+1)+(00(100)+(0(01(100)+1)(0(00(100)+1)0)))\) \((01(100)+1)+(00(100)+(0(01(100)+1)(0(00(00(100)+1))0)))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(\psi_0(\psi_2(0)))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega \times \psi_0(\Omega_2))}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)+10))\)
|
\((01(100)+1)+(100)\)
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\) \((01(100)+1)+(00(100)+(0(01(100)+1)(0(01(100)+1)0)))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega^{2})}\) |
\((01(100)+1)+(00(100)+(0(01(100)+1)+{\omega}0))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)0))\)
\((01(100)+1)+(00(100)+(0(01(100)+1)+10))\) \((01(100)+1)+(00(100)+(01(100)+1)+2)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2+\Omega^{\psi_0(\Omega_2+\Omega^{\omega})}\) |
\((01(100)+1)+(00(100)+(100))\)
|
\((01(100)+1)+(00(100)+(0(01(100)+1)+10))\)
\((01(100)+1)+(00(100)+(0(01(100)+1)+(00(100)+(0(01(100)+1)+10))0))\) \((01(100)+1)+(00(100)+(0(01(100)+1)+(00(100)+(0(01(100)+1)+(00(100)+(0(01(100)+1)+10))0))0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\Omega})\) |
\((01(100)+1)+(00(100)+(100))+(00(100)+(100))\)
|
\((01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+10))\)
\((01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+10))0))\) \((01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+(00(100)+(0(01(100)+1)+(00(100)+(100))+10))0))0))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\Omega} \times 2)\) |
\((01(100)+1)+(00(100)+(100)+1)\)
|
\((01(100)+1)+(00(100)+(100))\)
\((01(100)+1)+(00(100)+(100))+(00(100)+(100))\) \((01(100)+1)+(00(100)+(100))+(00(100)+(100))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2+\Omega^{\Omega} \times \omega)\) |
\((01(100)+1)+(00(00(100)+1))\)
|
\((01(100)+1)+(000)\)
\((01(100)+1)+(100)\) \((01(100)+1)+(00(100)+(100))\) \((01(100)+1)+(00(100)+(100)+(100))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2+\Omega^{\Omega+\omega})\) |
\((01(100)+1)+(00(00(00(100)+1)))\)
|
\((01(100)+1)+(00(000))\)
\((01(100)+1)+(100)\) \((01(100)+1)+(00(00(100)+(100)))\) \((01(100)+1)+(00(00(100)+(100)+(100)))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_1(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2+\Omega^{\Omega \times \omega})\) |
\((01(100)+1)+(01(100)+1)\)
|
\((01(100)+1)+(100)+1\)
\((01(100)+1)+(00(100)+1)\) \((01(100)+1)+(00(00(100)+1))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1})\) |
\((00(01(100)+1)+1)\)
|
\(0\)
\((01(100)+1)\) \((01(100)+1)+(01(100)+1)\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1} \times \omega)\) |
\((00(01(100)+1)+(00(100)+1))\)
|
\((01(100)+1)\)
\((00(01(100)+1)+(100))\) \((00(01(100)+1)+(100)+(100))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1} \times \Omega^{\omega})\) |
\((00(01(100)+1)+(00(00(100)+1)))\)
|
\((00(01(100)+1)+(000))\)
\((00(01(100)+1)+(100))\) \((00(01(100)+1)+(00(00(100)+(100))))\) \((00(01(100)+1)+(00(00(100)+(100)+(100))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_1(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1} \times \Omega^{\Omega^{\omega}})\) |
\((00(01(100)+1)+(00(00(00(100)+1))))\)
|
\((00(01(100)+1)+(00(000)))\)
\((00(01(100)+1)+(100))\) \((00(01(100)+1)+(00(00(00(100)+(100)))))\) \((00(01(100)+1)+(00(00(00(100)+(100)+(100)))))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_1(\psi_1(\psi_1(\psi_0(0))))))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1} \times \Omega^{\Omega^{\Omega^{\omega}}})\) |
\((00(01(100)+1)+(01(100)+1))\)
|
\((01(100)+1)+(100)+1\)
\((00(01(100)+1)+(00(100)+1))\) \((00(01(100)+1)+(00(00(100)+1)))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1}^2)\) |
\((00(00(01(100)+1)+1))\)
|
\((000)\)
\((01(100)+1)\) \((00(01(100)+1)+(01(100)+1))\) \((00(01(100)+1)+(01(100)+1)+(01(100)+1))\) |
\(\psi_0(\psi_2(0)+\psi_1(\psi_2(0)+\psi_1(\psi_2(0)+\psi_0(0))))\)
\(= \psi_0(\Omega_2+\varepsilon_{\Omega+1}^{\omega})\) |
\((01(100)+2))\)
|
\((01(100)+1)+1\)
\((00(01(100)+1)+1)\) \((00(00(01(100)+1)+1)))\) |
\(\psi_0(\psi_2(0)+\psi_2(0))\)
\(= \psi_0(\Omega_2+\Omega_2)\) |
\((01(100)+\omega))\)
|
\((100)\)
\((01(100)+1)\) \((01(100)+2)\) |
\(\psi_0(\psi_2(\psi_0(0)))\)
\(= \psi_0(\Omega_2 \times \omega)\) |
\((01(100)+(100)))\)
|
\((01(100)+(0(01(100)+1)0))\)
\((01(100)+(0(01(100)+(0(01(100)+1)0))0))\) \((01(100)+(0(01(100)+(0(01(100)+(0(01(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_1(0)))\)
\(= \psi_0(\Omega_2 \times \Omega)\) |
\((01(00(100)+1)))\)
|
\((100)\)
\((01(100)+(100))\) \((01(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_1(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2 \times \Omega \times \omega)\) |
\((01(00(00(100)+1))))\)
|
\((100)\)
\((01(00(100)+(100)))\) \((01(00(100)+(100)+(100)))\) |
\(\psi_0(\psi_2(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2 \times \Omega^{\omega})\) |
\((01(01(100)+1))\)
|
\((01(100)+1)\)
\((01(00(100)+1))\) \((01(00(00(100)+1)))\) |
\(\psi_0(\psi_2(\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2 \times \varepsilon_{\Omega+1})\) |
\((01(01(100)+\omega))\)
|
\((100)\)
\((01(01(100)+1))\) \((01(01(100)+2))\) |
\(\psi_0(\psi_2(\psi_1(\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2 \times \varepsilon_{\Omega+\omega})\) |
\((02(100)+1)\)
|
\((100)+1\)
\((01(100)+1)\) \((01(01(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(0)))\)
\(= \psi_0(\Omega_2^{2})\) |
\((02(100)+2)\)
|
\((02(100)+1)+1\)
\((01(02(100)+1)+1)\) \((01(01(02(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(0))+\psi_2(\psi_2(0)))\)
\(= \psi_0(\Omega_2^{2} \times 2)\) |
\((02(100)+\omega)\)
|
\((100)\)
\((02(100)+1)\) \((02(100)+2)\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{2} \times \omega)\) |
\((02(100)+(100))\)
|
\((02(100)+(0(02(100)+1)0))\)
\((02(100)+(0(02(100)+(0(02(100)+1)0))0))\) \((02(100)+(0(02(100)+(0(02(100)+(0(02(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{2} \times \Omega)\) |
\((02(00(100)+1))\)
|
\((100)\)
\((02(100)+(100))\) \((02(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_1(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{2} \times \Omega^{\omega})\) |
\((02(01(100)+1))\)
|
\((02(100)+1)\)
\((02(00(100)+1))\) \((02(00(00(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{2} \times \varepsilon_{\Omega+1})\) |
\((02(02(100)+1))\)
|
\((02(100)+1)\)
\((02(01(100)+1))\) \((02(01(01(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_1(\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{2} \times \psi_1(\Omega_2^{2}))\) |
\((03(100)+1)\)
|
\((100)+1\)
\((02(100)+1)\) \((02(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(0)+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{3})\) |
\((0\omega(100)+1)\)
|
\((00(100)+1)\)
\((01(100)+1)\) \((02(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\omega})\) |
\((0(010)(100)+1)\)
|
\((0\omega(100)+1)\)
\((0(00\omega)(100)+1)\) \((0(00(00\omega))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\varepsilon_0})\) |
\((0(0(010)0)(100)+1)\)
|
\((0(0\omega0)(100)+1)\)
\((0(0(00\omega)0)(100)+1)\) \((0(0(00(00\omega))0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_0(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\varepsilon_0}(0)})\) |
\((0(100)(100)+1)\)
|
\((00(100)+1)\)
\((01(100)+1)\) \((0(010)(100)+1)\) \((0(0(010)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_0})\) |
\((0(100)+1(100)+1)\)
|
\((100)+1\)
\((0(100)(100)+1)\) \((0(100)(0(100)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Gamma_0+1})\) |
\((0(100)+(0(100)0)(100)+1)\)
|
\((0(100)(100)+1)\)
\((0(100)+1(100)+1)\) \((0(100)+(010)(100)+1)\) \((0(100)+(0(010)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_0 \times 2})\) |
\((0(100)+(00(0(100)0)+1)(100)+1)\)
|
\((0(100)(100)+1)\)
\((0(100)+(0(100)0)(100)+1)\) \((0(100)+(0(100)0)+(0(100)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Gamma_0 \times \omega})\) |
\((0(100)+(00(0(100)0)+(0(100)0))(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(00(0(100)0)+1)(100)+1)\) \((0(100)+(00(0(100)0)+(010))(100)+1)\) \((0(100)+(00(0(100)0)+(0(010)0))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_0^{2}})\) |
\((0(100)+(00(00(0(100)0)+1))(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(00(0(100)0)+(0(100)0))(100)+1)\) \((0(100)+(00(0(100)0)+(0(100)0)+(0(100)0))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Gamma_0^{\omega}})\) |
\((0(100)+(01(0(100)0)+1)(100)+1)\)
|
\((0(100)+(0(100)0)+1(100)+1)\)
\((0(100)+(00(0(100)0)+1)(100)+1)\) \((0(100)+(00(00(0(100)0)+1))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\varepsilon_{\Gamma_0+1}})\) |
\((0(100)+(02(0(100)0)+1)(100)+1)\)
|
\((0(100)+(0(100)0)+1(100)+1)\)
\((0(100)+(01(0(100)0)+1)(100)+1)\) \((0(100)+(01(01(0(100)0)+1))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\zeta_{\Gamma_0+1}})\) |
\((0(100)+(0\omega(0(100)0)+1)(100)+1)\)
|
\((0(100)+(00(0(100)0)+1)(100)+1)\)
\((0(100)+(01(0(100)0)+1)(100)+1)\) \((0(100)+(02(0(100)0)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\omega}(\Gamma_0+1)})\) |
\((0(100)+(0(100)1)(100)+1)\)
|
\((0(100)+(00(0(100)0)+1)(100)+1)\)
\((0(100)+(01(0(100)0)+1)(100)+1)\) \((0(100)+(0(010)(0(100)0)+1)(100)+1)\) \((0(100)+(0(0(010)0)(0(100)0)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0}(1)})\) |
\((0(100)+(0(100)\omega)(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(0(100)1)(100)+1)\) \((0(100)+(0(100)2)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0}(\omega)})\) |
\((0(100)+(0(100)(0(100)0))(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(0(100)1)(100)+1)\) \((0(100)+(0(100)(010))(100)+1)\) \((0(100)+(0(100)(0(010)0))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_0(\psi_1(\psi_1(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0}(\Gamma_0)})\) |
\((0(100)+(0(100)+10)(100)+1)\)
|
\((0(100)(100)+1)\)
\((0(100)+(0(100)0)(100)+1)\) \((0(100)+(0(100)(0(100)0))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0+1}(0)})\) |
\((0(100)+(0(100)+(0(100)0)0)(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(0(100)+10)(100)+1)\) \((0(100)+(0(100)+(010)0)(100)+1)\) \((0(100)+(0(100)+(0(010)0)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))+\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0 \times 2}(0)})\) |
\((0(100)+(0(100)+(00(0(100)0)+1)0)(100)+1)\)
|
\((0(100)+(0(100)0)(100)+1)\)
\((0(100)+(0(100)+(0(100)0)0)(100)+1)\) \((0(100)+(0(100)+(0(100)0)+(0(100)0)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0 \times \omega}(0)})\) |
\((0(100)+(0(100)+(00(0(100)0)+(0(100)0))0)(100)+1)\)
|
\((0(100)+(0(100)+(0(100)0)0)(100)+1)\)
\((0(100)+(0(100)+(00(0(100)0)+1)0)(100)+1)\) \((0(100)+(0(100)+(00(0(100)0)+(010))0)(100)+1)\) \((0(100)+(0(100)+(00(0(100)0)+(0(010)0))0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0))))+\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0^{2}}(0)})\) |
\((0(100)+(0(100)+(00(00(0(100)0)+1))0)(100)+1)\)
|
\((0(100)+(0(100)+(000)0)(100)+1)\)
\((0(100)+(0(100)+(0(100)0)0)(100)+1)\) \((0(100)+(0(100)+(00(0(100)0)+(0(100)0)))0)(100)+1)\) \((0(100)+(0(100)+(00(0(100)0)+(0(100)0)+(0(100)0))0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\Gamma_0^{\omega}}(0)})\) |
\((0(100)+(0(100)+(01(0(100)0)+1)0)(100)+1)\)
|
\((0(100)+(0(100)+(0(100)0)+10)(100)+1)\)
\((0(100)+(0(100)+(00(0(100)+(0(100)0)+1))0)(100)+1)\) \((0(100)+(0(100)+(00(00(0(100)+(0(100)0)+1)))0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\varepsilon_{\Gamma_0+1}}(0)})\) |
\((0(100)+(0(100)+(02(0(100)0)+1)0)(100)+1)\)
|
\((0(100)+(0(100)+(0(100)0)+10)(100)+1)\)
\((0(100)+(0(100)+(01(0(100)+(0(100)0)+1))0)(100)+1)\) \((0(100)+(0(100)+(01(01(0(100)+(0(100)0)+1)))0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\zeta_{\Gamma_0+1}}(0)})\) |
\((0(100)+(0(100)+(0\omega(0(100)0)+1)0)(100)+1)\)
|
\((0(100)+(0(100)+(00(0(100)0)+1)0)(100)+1)\)
\((0(100)+(0(100)+(01(0(100)0)+1)0)(100)+1)\) \((0(100)+(0(100)+(02(0(100)0)+1)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(0))))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\varphi_{\omega}(\Gamma_0+1)}(0)})\) |
\((0(100)+(0(100)+(0(100)1)0)(100)+1)\)
|
\((0(100)+(0(100)+(00(0(100)0)+1)0)(100)+1)\)
\((0(100)+(0(100)+(01(0(100)0)+1)0)(100)+1)\) \((0(100)+(0(100)+(0(010)(0(100)0)+1)0)(100)+1)\) \((0(100)+(0(100)+(0(0(010)0)(0(100)0)+1)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))))))))\)
\(= \psi_0(\Omega_2^{\varphi_{\varphi_{\Gamma_0}(1)}(0)})\) |
\((0(100)+(100)(100)+1)\)
|
\((0(100)+(0(100)+10)(100)+1)\)
\((0(100)+(0(100)+(0(100)+10)0)(100)+1)\) \((0(100)+(0(100)+(0(100)+(0(100)+10)0)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))+\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_1})\) |
\((0(00(100)+1)(100)+1)\)
|
\((00(100)+1)\)
\((0(100)(100)+1)\) \((0(100)+(100)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Gamma_{\omega}})\) |
\((0(00(100)+2)(100)+1)\)
|
\((00(100)+1)\)
\((0(00(100)+1)(100)+1)\) \((0(00(100)+1)+(00(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(0)+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Gamma_{\omega \times 2}})\) |
\((0(00(100)+\omega)(100)+1)\)
|
\((0(100)(100)+1)\)
\((0(00(100)+1)(100)+1)\) \((0(00(100)+2)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_{\omega^{2}}})\) |
\((0(00(100)+(010))(100)+1)\)
|
\((0(00(100)+\omega)0(100)+1)\)
\((0(00(100)+(00\omega))(100)+1)\) \((0(00(100)+(00(00\omega)))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_0(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Gamma_{\varepsilon_0}})\) |
\((0(00(100)+(100))(100)+1)\)
|
\((0(00(100)+(0(00(100)+1)0))(100)+1)\)
\((0(00(100)+(0(00(100)+(0(00(100)+1)0))0))(100)+1)\) \((0(00(100)+(0(00(100)+(0(00(100)+(0(00(100)+1)0))0))0))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega+1})})\) |
\((0(00(00(100)+1))(100)+1)\)
|
\((0(000)(100)+1)\)
\((0(100)(100)+1)\) \((0(00(100)+(100))(100)+1)\) \((0(00(100)+(100)+(100))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega+\omega})})\) |
\((0(00(00(100)+(100)))(100)+1)\)
|
\((0(00(00(100)+(0(00(100)+1)0)))(100)+1)\)
\((0(00(00(100)+(0(00(100)+(0(00(100)+1)0))0)))(100)+1)\) \((0(00(00(100)+(0(00(100)+(0(00(100)+(0(00(100)+1)0))0))0)))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))+\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega \times 2})})\) |
\((0(00(00(00(100)+1)))(100)+1)\)
|
\((0(00(000))(100)+1)\)
\((0(100)(100)+1)\) \((0(00(00(100)+(100)))(100)+1)\) \((0(00(00(100)+(100)+(100)))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega \times \omega})})\) |
\((0(00(00(00(100)+(100))))(100)+1)\)
|
\((0(00(00(00(100)+(0(00(100)+1)0))))(100)+1)\)
\((0(00(00(00(100)+(0(00(100)+(0(00(100)+1)0))0))))(100)+1)\) \((0(00(00(00(100)+(0(00(100)+(0(00(100)+(0(00(100)+1)0))0))0))))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)+\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega^{2}})})\) |
\((0(00(00(00(00(100)+1))))(100)+1)\)
|
\((0(00(00(000)))(100)+1)\)
\((0(100)(100)+1)\) \((0(00(00(00(100)+(100))))(100)+1)\) \((0(00(00(00(100)+(100)+(100))))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\Omega^{\Omega^{\omega}})})\) |
\((0(01(100)+1)(100)+1)\)
|
\((0(100)+1(100)+1)\)
\((0(00(100)+1)(100)+1)\) \((0(00(00(100)+1))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\psi_0(\varepsilon_{\Omega+1})})\) |
\((0(02(100)+1)(100)+1)\)
|
\((0(100)+1(100)+1)\)
\((0(01(100)+1)(100)+1)\) \((0(01(01(100)+1))(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\zeta_{\Omega+1})})\) |
\((0(0\omega(100)+1)(100)+1)\)
|
\((0(00(100)+1)(100)+1)\)
\((0(01(100)+1)(100)+1)\) \((0(02(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\varphi_{\omega}(\Omega+1))})\) |
\((0(0(100)(100)+1)(100)+1)\)
|
\((0(00(100)+1)(100)+1)\)
\((0(01(100)+1)(100)+1)\) \((0(0(010)(100)+1)(100)+1)\) \((0(0(0(010)0)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\varphi_{\Gamma_0}(\Omega+1))})\) |
\((0(0(0(100)(100)+1)(100)+1)(100)+1)\)
|
\((0(0(00(100)+1)(100)+1)(100)+1)\)
\((0(0(01(100)+1)(100)+1)(100)+1)\) \((0(0(0(010)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))))))))\)
\(= \psi_0(\Omega_2^{\psi_0(\varphi_{\psi_0(\Omega_2^{\psi_0(\varphi_{\Gamma_0}(\Omega+1))})}(\Omega+1))})\) |
\((101)\)
|
\((0(100)(100)+1)\)
\((0(0(100)(100)+1)(100)+1)\) \((0(0(0(100)(100)+1)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega})\) |
\((01(101)+1)\)
|
\((00(101)+1)\)
\((00(00(101)+1))\) \((00(00(00(101)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2)\) |
\((02(101)+1)\)
|
\((101)+1\)
\((01(101)+1)\) \((01(01(101)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2^{2})\) |
\((0\omega(101)+1)\)
|
\((00(101)+1)\)
\((01(101)+1)\) \((02(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2^{\omega})\) |
\((0(100)(101)+1)\)
|
\((00(101)+1)\)
\((01(101)+1)\) \((0(010)(101)+1)\) \((0(0(010)0)(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2^{\Gamma_0})\) |
\((0(101)(101)+1)\)
|
\((0(0(100)(100)+1)(101)+1)\)
\((0(0(0(100)(100)+1)(100)+1)(101)+1)\) \((0(0(0(0(100)(100)+1)(100)+1)(100)+1)(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})})\) |
\((0(0(101)(101)+1)(101)+1)\)
|
\((0(0(0(100)(100)+1)(101)+1)(101)+1)\)
\((0(0(0(0(100)(100)+1)(100)+1)(101)+1)(101)+1)\) \((0(0(0(0(0(100)(100)+1)(100)+1)(100)+1)(101)+1)(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})})})\) |
\((102)\)
|
\((0(101)(101)+1)\)
\((0(0(101)(101)+1)(101)+1)\) \((0(0(0(101)(101)+1)(101)+1)(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega} \times 2)\) |
\((10\omega)\)
|
\((100)\)
\((101)\) \((102)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega} \times \omega)\) |
\((10(100))\)
|
\((10(0(101)0))\)
\((10(0(10(0(101)0))0))\) \((10(0(10(0(10(0(101)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega} \times \Omega)\) |
\((10(0\omega(100)+1))\)
|
\((10(00(100)+1))\)
\((10(01(100)+1))\) \((10(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \varphi_{\omega}(\Omega+1))\) |
\((10(101))\)
|
\((10(0(100)(100)+1))\)
\((10(0(0(100)(100)+1)(100)+1))\) \((10(0(0(0(100)(100)+1)(100)+1)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}))\) |
\((10(102))\)
|
\((10(0(101)(101)+1))\)
\((10(0(0(101)(101)+1)(101)+1))\) \((10(0(0(0(101)(101)+1)(101)+1)(101)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times 2)}))\) |
\((10(10\omega))\)
|
\((10(100))\)
\((10(101))\) \((10(102))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \omega)}))\) |
\((10(10(0(10(100))0))\)
|
\((10(10(0(10(0(101)0))0)))\)
\((10(10(0(10(0(10(0(101)0))0))0)))\) \((10(10(0(10(0(10(0(10(0(101)0))0))0))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega)}))\) |
\((10(10(100)))\)
|
\((10(10(0(10(101))0)))\)
\((10(10(0(10(10(0(10(101))0)))0)))\) \((10(10(0(10(10(0(10(10(0(10(101))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}))\) |
\((10(10(100))+\omega)\)
|
\((10(10(100)))\)
\((10(10(100))+1)\) \((10(10(100))+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega})+\omega))\) |
\((10(10(100))+(0\omega(100)+1))\)
|
\((10(10(100))+(00(100)+1))\)
\((10(10(100))+(01(100)+1))\) \((10(10(100))+(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega})+\psi_1(\Omega_2^{\omega})))\) |
\((10(10(100))+(101))\)
|
\((10(10(100))+(0(100)(100)+1))\)
\((10(10(100))+(0(0(100)(100)+1)(100)+1))\) \((10(10(100))+(0(0(0(100)(100)+1)(100)+1)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega})+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})})))\) |
\((10(10(100))+(10\omega))\)
|
\((10(10(100))+(100))\)
\((10(10(100))+(101))\) \((10(10(100))+(102))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega})+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \omega)})))\) |
\((10(10(100))+(10(0(10(100))0)))\)
|
\((10(10(100))+(10(0(10(0(10(0(101)0))0))0)))\)
\((10(10(100))+(10(0(10(0(10(0(10(0(10(0(101)0))0))0))0))0)))\) \((10(10(100))+(10(0(10(0(10(0(10(0(10(0(10(0(10(0(101)0))0))0))0))0))0))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega})+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega)})))\) |
\((10(10(100))+(10(100)))\)
|
\((10(10(100))+(10(0(10(10(100))+(101))0)))\)
\((10(10(100))+(10(0(10(10(100))+(10(0(10(10(100))+(101))0)))0)))\) \((10(10(100))+(10(0(10(10(100))+(10(0(10(10(100))+(10(0(10(10(100))+(101))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}) \times 2)\) |
\((10(00(10(100))+1))\)
|
\((100)\)
\((10(10(100)))\) \((10(10(100))+(10(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}) \times \omega)\) |
\((10(00(00(10(100))+1)))\)
|
\((10(000))\)
\((10(10(100)))\) \((10(00(10(100))+(10(100))))\) \((10(00(10(100))+(10(100))+(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega})^{\omega})\) |
\((10(01(10(100))+1))\)
|
\((10(10(100))+1)\)
\((10(00(10(100))+1))\) \((10(00(00(10(100))+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2))\) |
\((10(01(10(100))+\omega))\)
|
\((10(10(100)))\)
\((10(01(10(100))+1))\) \((10(01(10(100))+2))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \omega))\) |
\((10(01(10(100))+(100)))\)
|
\((10(01(10(100))+(0(10(01(10(100))+1))0)))\)
\((10(01(10(100))+(0(10(01(10(100))+(0(10(01(10(100))+1))0)))0)))\) \((10(01(10(100))+(0(10(01(10(100))+(0(10(01(10(100))+(0(10(01(10(100))+1))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \Omega))\) |
\((10(01(10(100))+(0\omega(100)+1)))\)
|
\((10(01(10(100))+(00(100)+1)))\)
\((10(01(10(100))+(01(100)+1)))\) \((10(01(10(100))+(02(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\omega})))\) |
\((10(01(10(100))+(101)))\)
|
\((10(01(10(100))+(0(100)(100)+1)))\)
\((10(01(10(100))+(0(0(100)(100)+1)(100)+1)))\) \((10(01(10(100))+(0(0(0(100)(100)+1)(100)+1)(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})})))\) |
\((10(01(10(100))+(10\omega)))\)
|
\((10(01(10(100))+(100)))\)
\((10(01(10(100))+(101)))\) \((10(01(10(100))+(102)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \omega)})))\) |
\((10(01(10(100))+(10(0(10(100))0))))\)
|
\((10(01(10(100))+(10(0(10(0(101)0))0))))\)
\((10(01(10(100))+(10(0(10(0(10(0(101)0))0))0))))\) \((10(01(10(100))+(10(0(10(0(10(0(10(0(101)0))0))0))0))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega)})))\) |
\((10(01(10(100))+(10(100))))\)
|
\((10(01(10(100))+(10(0(10(01(10(100))+(101)))0))))\)
\((10(01(10(100))+(10(0(10(01(10(100))+(10(0(10(01(10(100))+(101)))0))))0))))\) \((10(01(10(100))+(10(0(10(01(10(100))+(10(0(10(01(10(100))+(10(0(10(01(10(100))+(101)))0))))0))))0))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\Omega})))\) |
\((10(01(00(10(100))+1)))\)
|
\((10(010))\)
\((10(10(100)))\) \((10(01(10(100))+(10(100))))\) \((10(01(10(100))+(10(100))+(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\Omega})^{\omega}))\) |
\((10(01(01(10(100))+1)))\)
|
\((10(01(10(100))+1))\)
\((10(01(00(10(100))+1)))\) \((10(01(00(00(10(100))+1))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2 \times \psi_1(\Omega_2^{\Omega}+\Omega_2)))\) |
\((10(02(10(100))+1))\)
|
\((10(10(100))+1)\)
\((10(01(10(100))+1))\) \((10(01(01(10(100))+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{2}))\) |
\((10(0\omega(10(100))+1))\)
|
\((10(00(10(100))+1))\)
\((10(01(10(100))+1))\) \((10(02(10(100))+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\omega}))\) |
\((10(0(10(100))(10(100))+1))\)
|
\((10(0(10(0(101)0))(10(100))+1))\)
\((10(0(10(0(10(0(101)0))0))(10(100))+1))\) \((10(0(10(0(10(0(10(0(101)0))0))0))(10(100))+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega)}))\) |
\((10(10(100)+1))\)
|
\((10(0(10(100))(10(100))+1))\)
\((10(0(0(10(100))(10(100))+1)(10(100))+1))\) \((10(0(0(0(10(100))(10(100))+1)(10(100))+1)(10(100))+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0)+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega \times \omega)}))\) |
\((10(10(100)+(0(10(100)+(100))0)))\)
|
\((10(10(100)+(0(10(100)+(0(10(100)+1)0))0)))\)
\((10(10(100)+(0(10(100)+(0(10(100)+(0(10(100)+1)0))0))0)))\) \((10(10(100)+(0(10(100)+(0(10(100)+(0(10(100)+(0(10(100)+1)0))0))0))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0)+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega^{2})}))\) |
\((10(10(100)+(100)))\)
|
\((10(10(100)+(0(10(10(100)+1))0)))\)
\((10(10(100)+(0(10(10(100)+(0(10(10(100)+1))0)))0)))\) \((10(10(100)+(0(10(10(100)+(0(10(10(100)+(0(10(10(100)+1))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times 2))\) |
\((10(10(00(100)+1)))\)
|
\((10(100))\)
\((10(10(100)))\) \((10(10(100)+(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \omega))\) |
\((10(10(01(100)+1)))\)
|
\((10(10(100)+1))\)
\((10(10(00(100)+1)))\) \((10(10(00(00(100)+1))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2)))\) |
\((10(10(01(100)+1)))\)
|
\((10(10(100)+1))\)
\((10(10(00(100)+1)))\) \((10(10(00(00(100)+1))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2)))\) |
\((10(10(02(100)+1)))\)
|
\((10(10(100)+1))\)
\((10(10(01(100)+1)))\) \((10(10(01(01(100)+1))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{2})))\) |
\((10(10(0\omega(100)+1)))\)
|
\((10(10(00(100)+1)))\)
\((10(10(01(100)+1)))\) \((10(10(02(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\omega})))\) |
\((10(10(101)))\)
|
\((10(10(0(100)(100)+1)))\)
\((10(10(0(0(100)(100)+1)(100)+1)))\) \((10(10(0(0(0(100)(100)+1)(100)+1)(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})})))\) |
\((10(10(10\omega)))\)
|
\((10(10(100)))\)
\((10(10(101)))\) \((10(10(102)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \omega)})))\) |
\((10(10(10(100))))\)
|
\((10(10(10(0(10(10(101)))0))))\)
\((10(10(10(0(10(10(10(0(10(10(101)))0))))0))))\) \((10(10(10(0(10(10(10(0(10(10(10(0(10(10(101)))0))))0))))0))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times 2)))\) |
\((200)\)
|
\(0)\)
\((100)\) \((10(100))\) \((10(10(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1})\) |
\((200)+(0(200)0)\)
|
\((200)+(000))\)
\((200)+(0(100)0)\) \((200)+(0(10(100))0)\) \((200)+(0(10(10(100)))0)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))+\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}) \times 2\) |
\((200)+(00(0(200)0)+1)\)
|
\((200))\)
\((200)+(0(200)0)\) \((200)+(0(200)0)+(0(200)0)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_0(0))\)
\(= \psi_0(\Omega_2^{\Omega+1}) \times \omega\) |
\((200)+(01(0(200)0)+1)\)
|
\((200)+(0(200)0)+1)\)
\((200)+(00(0(200)0)+1)\) \((200)+(00(00(0(200)0)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(0))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega)\) |
\((200)+(02(0(200)0)+1)\)
|
\((200)+(0(200)0)+1)\)
\((200)+(01(0(200)0)+1)\) \((200)+(01(01(0(200)0)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{2})\) |
\((200)+(0\omega(0(200)0)+1)\)
|
\((200)+(00(0(200)0)+1))\)
\((200)+(01(0(200)0)+1)\) \((200)+(02(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\omega})\) |
\((200)+(0(100)(0(200)0)+1)\)
|
\((200)+(00(0(200)0)+1))\)
\((200)+(01(0(200)0)+1)\) \((200)+(0(010)(0(200)0)+1)\) \((200)+(0(0(010)0)(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\Gamma_0})\) |
\((200)+(0(101)(0(200)0)+1)\)
|
\((200)+(0(0(100)(100)+1)(0(200)0)+1))\)
\((200)+(0(0(0(100)(100)+1)(100)+1)(0(200)0)+1)\) \((200)+(0(0(0(0(100)(100)+1)(100)+1)(100)+1)(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega})})\) |
\((200)+(0(10\omega)(0(200)0)+1)\)
|
\((200)+(0(100)(0(200)0)+1))\)
\((200)+(0(101)(0(200)0)+1)\) \((200)+(0(102)(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega} \times \omega)})\) |
\((200)+(0(10(100))(0(200)0)+1)\)
|
\((200)+(0(10(0(101)0))(0(200)0)+1))\)
\((200)+(0(10(0(10(0(101)0))0))(0(200)0)+1)\) \((200)+(0(10(0(10(0(10(0(101)0))0))0))(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega} \times \Omega)})\) |
\((200)+(0(10(10(100)))(0(200)0)+1)\)
|
\((200)+(0(10(10(0(10(101))0)))(0(200)0)+1))\)
\((200)+(0(10(10(0(10(10(0(10(101))0)))0)))(0(200)0)+1)\) \((200)+(10(10(0(10(10(0(10(10(0(10(101))0)))0)))0)))(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \Omega))})\) |
\((200)+(0(200)1)\)
|
\((200)+(00(0(200)0)+1))\)
\((200)+(0(100)(0(200)0)+1)\) \((200)+(10(100))(0(200)0)+1)\) \((200)+(10(10(100)))(0(200)0)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})})\) |
\((200)+(0(200)2)\)
|
\((200)+(00(0(200)1)+1))\)
\((200)+(0(100)(0(200)1)+1)\) \((200)+(10(100))(0(200)1)+1)\) \((200)+(10(10(100)))(0(200)1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})} \times 2)\) |
\((200)+(0(200)\omega)\)
|
\((200)+(0(200)0)\)
\((200)+(0(200)1)\) \((200)+(0(200)2) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})} \times \omega)\) |
\((200)+(0(200)(0(200)0))\)
|
\((200)+(0(200)(000)))\)
\((200)+(0(200)(0(100)0))\) \((200)+(0(200)+(0(200)(0(10(100))0))) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})} \times \psi_0(\Omega_2^{\Omega+1}))\) |
\((200)+(100)\)
|
\((200)\)
\((200)+(0(200)0)\) \((200)+(0(200)(0(200)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})+1})\) |
\((200)+(100)+(100)\)
|
\((200)+(100)+(0(200)+(100)+10)\)
\((200)+(100)+(0(200)+(100)+(0(200)+(100)+10)0)\) \((200)+(100)+(0(200)+(100)+(0(200)+(100)+(0(200)+(100)+10)0)0)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_1(0)+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})+2})\) |
\((200)+(00(100)+1)\)
|
\((200)\)
\((200)+(100)\) \((200)+(100)+(100)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})+\omega})\) |
\((200)+(00(100)+(0(200)0))\)
|
\((200)+(00(100)+(000))\)
\((200)+(00(100)+(0(100)0))\) \((200)+(00(100)+(0(10(100))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1}) \times 2})\) |
\((200)+(00(100)+(00(0(200)0)+1))\)
|
\((200)+(100)\)
\((200)+(00(100)+(0(200)0))\) \((200)+(00(100)+(0(200)0)+(0(200)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1}) \times \omega})\) |
\((200)+(00(100)+(00(0(200)0)+(0(200)0)))\)
|
\((200)+(00(100)+(00(0(200)0)+(000)))\)
\((200)+(00(100)+(00(0(200)0)+(0(100)0)))\) \((200)+(00(100)+(00(0(200)0)+(0(10(100))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))+\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})^{2}})\) |
\((200)+(00(100)+(00(00(0(200)0)+1)))\)
|
\((200)+(00(100)+(000))\)
\((200)+(00(100)+(0(200)0))\) \((200)+(00(100)+(00(0(200)0)+(0(200)0)))\) \((200)+(00(100)+(00(0(200)0)+(0(200)0)+(0(200)0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1})^{\omega}})\) |
\((200)+(00(100)+(01(0(200)0)+1))\)
|
\((200)+(00(100)+(0(200)0)+1)\)
\((200)+(00(100)+(00(0(200)0)+1))\) \((200)+(00(100)+(00(00(0(200)0)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\psi_0(\Omega_2^{\Omega+1}+\Omega)})\) |
\((200)+(00(100)+(100))\)
|
\((200)+(00(100)+(0(200)+(00(100)+1)0))\)
\((200)+(00(100)+(0(200)+(00(100)+(0(200)+(00(100)+1)0))0))\) \((200)+(00(100)+(0(200)+(00(100)+(0(200)+(00(100)+(0(200)+(00(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\Omega})\) |
\((200)+(00(00(100)+1))\)
|
\((200)+(000)\)
\((200)+(100)\) \((200)+(00(100)+(100))\) \((200)+(00(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_1(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega^{\Omega^{\omega}})\) |
\((200)+(01(100)+1)\)
|
\((200)+(100)+1\)
\((200)+(00(100)+1)\) \((200)+(00(00(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\varepsilon_{\Omega+1})\) |
\((200)+(02(100)+1)\)
|
\((200)+(100)+1\)
\((200)+(01(100)+1)\) \((200)+(01(01(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\zeta_{\Omega+1})\) |
\((200)+(0\omega(100)+1)\)
|
\((200)+(00(100)+1)\)
\((200)+(01(100)+1)\) \((200)+(02(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\varphi_{\omega}(\Omega+1))\) |
\((200)+(0(100)(100)+1)\)
|
\((200)+(00(100)+1)\)
\((200)+(01(100)+1)\) \((200)+(0(010)(100)+1)\) \((200)+(0(0(010)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\varphi_{\Gamma}(\Omega+1))\) |
\((200)+(0(0(100)(100)+1)(100)+1)\)
|
\((200)+(0(00(100)+1)(100)+1)\)
\((200)+(0(01(100)+1)(100)+1)\) \((200)+(0(0(010)(100)+1)(100)+1)\) \((200)+(0(0(0(010)0)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Gamma_0})}))\) |
\((200)+(0(101)(100)+1)\)
|
\((200)+(0(100)(100)+1)\)
\((200)+(0(0(100)(100)+1)(100)+1)\) \((200)+(0(0(0(100)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}))\) |
\((200)+(0(101)(100)+2)\)
|
\((200)+(0(100)(0(101)(100)+1)+1)\)
\((200)+(0(0(100)(0(101)(100)+1)+1)(0(101)(100)+1)+1)\) \((200)+(0(0(0(100)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})} \times 2))\) |
\((200)+(0(101)(100)+\omega)\)
|
\((200)+(100)\)
\((200)+(0(101)(100)+1)\) \((200)+(0(101)(100)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})} \times \omega))\) |
\((200)+(0(101)(100)+(100))\)
|
\((200)+(0(101)(100)+(0(101)+(0(101)(100)+1)0))\)
\((200)+(0(101)(100)+(0(101)+(0(101)(100)+(0(101)+(0(101)(100)+1)0))0))\) \((200)+(0(101)(100)+(0(101)+(0(101)(100)+(0(101)+(0(101)(100)+(0(101)+(0(101)(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}+\Omega))\) |
\((200)+(0(101)(01(100)+1))\)
|
\((200)+(0(101)(100)+1)\)
\((200)+(0(101)(00(100)+1))\) \((200)+(0(101)(00(00(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}+\varepsilon_{\Omega+1}))\) |
\((200)+(0(101)(02(100)+1))\)
|
\((200)+(0(101)(100)+1)\)
\((200)+(0(101)(01(100)+1))\) \((200)+(0(101)(01(01(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(\psi_2(\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}+\zeta_{\Omega+1}))\) |
\((200)+(0(101)(0\omega(100)+1))\)
|
\((200)+(0(101)(00(100)+1))\)
\((200)+(0(101)(01(100)+1))\) \((200)+(0(101)(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(\psi_2(\psi_2(\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}+\varphi_{\omega}(\Omega+1)))\) |
\((200)+(0(101)(0(101)(100)+1))\)
|
\((200)+(0(101)(0(0(100)(100)+1)(100)+1))\)
\((200)+(0(101)(0(0(100)(100)+1)(100)+1))\) \((200)+(0(101)(0(0(0(100)(100)+1)(100)+1)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})})))\) |
\((200)+(0(101)+1(100)+1)\)
|
\((200)+(100)+1)\)
\((200)+(0(101)(100)+1)\) \((200)+(0(101)(0(101)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})+1}))\) |
\((200)+(0(101)+2(100)+1)\)
|
\((200)+(100)+1\)
\((200)+(0(101)+1(100)+1)\) \((200)+(0(101)+1(0(101)+1(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(0)+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})+2}))\) |
\((200)+(0(101)+\omega(100)+1)\)
|
\((200)+(0(101)(100)+1)\)
\((200)+(0(101)+1(100)+1)\) \((200)+(0(101)+2(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})+\omega}))\) |
\((200)+(0(101)+(00(0(101)0)+1)(100)+1)\)
|
\((200)+(0(101)(100)+1)\)
\((200)+(0(101)+(0(101)0)(100)+1)\) \((200)+(0(101)+(0(101)0)+(0(101)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega}) \times \omega}))\) |
\((200)+(0(101)+(01(0(101)0)+1)(100)+1)\)
|
\((200)+(0(101)+(0(101)0)+1(100)+1)\)
\((200)+(0(101)+(00(0(101)0)+1)(100)+1)\) \((200)+(0(101)+(00(0(101)0)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega}+\Omega)}))\) |
\((200)+(0(101)+(100)(100)+1)\)
|
\((200)+(0(101)+(0(200)+(0(101)+1(100)+1)0)(100)+1)\)
\((200)+(0(101)+(0(200)+(0(101)+(0(200)+(0(101)+1(100)+1)0)(100)+1)0)(100)+1)\) \((200)+(0(101)+(0(200)+(0(101)+(0(200)+(0(101)+(0(200)+(0(101)+1(100)+1)0)(100)+1)0)(100)+1)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}))\) |
\((200)+(00(0(101)+(100)(100)+1)+1)\)
|
\((200))\)
\((200)+(0(101)+(100)(100)+1)\) \((200)+(0(101)+(100)(100)+1)+(0(101)+(100)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}) \times \omega)\) |
\((200)+(01(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)+(100)(100)+1)+1\)
\((200)+(00(0(101)+(100)(100)+1)+1)\) \((200)+(00(00(0(101)+(100)(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2))\) |
\((200)+(0\omega(0(101)+(100)(100)+1)+1)\)
|
\((200)+(00(0(101)+(100)(100)+1)+1)\)
\((200)+(01(0(101)+(100)(100)+1)+1)\) \((200)+(02(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\omega}))\) |
\((200)+(0(101)(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(0(100)(100)+1)(0(101)+(100)(100)+1)+1)\)
\((200)+(0(0(0(100)(100)+1)(100)+1)(0(101)+(100)(100)+1)+1)\) \((200)+(0(0(0(0(100)(100)+1)(100)+1)(100)+1)(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})}))\) |
\((200)+(0(101)+1(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)+(100)(100)+1)+1\)
\((200)+(0(101)(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)(0(101)(0(101)+(100)(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})+1}))\) |
\((200)+(0(101)+2(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)+(100)(100)+1)+1\)
\((200)+(0(101)+1(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)+1(0(101)+1(0(101)+(100)(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(0)+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})+2}))\) |
\((200)+(0(101)+\omega(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)(0(101)+(100)(100)+1)+1)\)
\((200)+(0(101)+1(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)+2(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\omega))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega})+\omega}))\) |
\((200)+(0(101)+(00(0(101)0)+1)(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)(0(101)+(100)(100)+1)+1)\)
\((200)+(0(101)+(0(101)0)(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)+(0(101)0)+(0(101)0)(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega}) \times \omega}))\) |
\((200)+(0(101)+(01(0(101)0)+1)(0(101)+(100)(100)+1)+1)\)
|
\((200)+(0(101)+(0(101)0)+1(0(101)+(100)(100)+1)+1)\)
\((200)+(0(101)+(00(0(101)0)+1)(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)+(00(00(0(101)0)+1))(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega}+\Omega_2^{\psi_0(\Omega_2^{\Omega}+\Omega)}))\) |
\((200)+(0(101)+(100)(100)+2)\)
|
\((200)+(0(101)+(0(101)+10)(0(101)+(100)(100)+1)+1)\)
\((200)+(0(101)+(0(101)+(0(101)+10)0)(0(101)+(100)(100)+1)+1)\) \((200)+(0(101)+(0(101)+(0(101)+(0(101)+10)0)0)(0(101)+(100)(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega} \times 2))\) |
\((200)+(0(101)+(100)(100)+\omega)\)
|
\((200)+(100)\)
\((200)+(0(101)+(100)(100)+1)\) \((200)+(0(101)+(100)(100)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega} \times \omega))\) |
\((200)+(0(101)+(100)(100)+(100))\)
|
\((200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+1)0))\)
\((200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+1)0))0))\) \((200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+(0(200)+(0(101)+(100)(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega} \times \Omega))\) |
\((200)+(0(101)+(100)(00(100)+1))\)
|
\((200)+(0(101)+(100)0)\)
\((200)+(100)\) \((200)+(0(101)+(100)(100)+(100))\) \((200)+(0(101)+(100)(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega} \times \Omega^{\omega}))\) |
\((200)+(0(101)+(100)(0(101)+(100)(100)+1))\)
|
\((200)+(0(101)+(100)(0(101)+(0(101)+10)(100)+1))\)
\((200)+(0(101)+(100)(0(101)+(0(101)+(0(101)+10)0)(100)+1))\) \((200)+(0(101)+(100)(0(101)+(0(101)+(0(101)+(0(101)+10)0)0)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1)+\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega} \times \Omega)})))\) |
\((200)+(0(101)+(100)+1(100)+1)\)
|
\((200)+(0(101)+(100)(100)+1)\)
\((200)+(0(101)+(100)(100)+1)\) \((200)+(0(101)+(100)(0(101)+(100)(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}))\) |
\((200)+(0(101)+(100)+1(100)+2)\)
|
\((200)+(0(101)+(100)(0(101)+(100)+1(100)+1)+1)\)
\((200)+(0(101)+(100)(0(101)+(100)+1(100)+1)+1)\) \((200)+(0(101)+(100)(0(101)+(100)(0(101)+(100)+1(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times 2)\) |
\((200)+(0(101)+(100)+1(100)+\omega)\)
|
\((200)+(100)\)
\((200)+(0(101)+(100)+1(100)+1)\) \((200)+(0(101)+(100)+1(100)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times \omega)\) |
\((200)+(0(101)+(100)+1(100)+(100))\)
|
\((200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+1)0))\)
\((200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+1)0))0))\) \((200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+(0(200)+(0(101)+(100)+1(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times \Omega)\) |
\((200)+(0(101)+(100)+1(00(100)+1))\)
|
\((200)+(0(101)+(100)+10)\)
\((200)+(100)\) \((200)+(0(101)+(100)+1(100)+(100))\) \((200)+(0(101)+(100)+1(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times \Omega^{\omega})\) |
\((200)+(0(101)+(100)+1(0(101)+(100)+1(100)+1))\)
|
\((200)+(0(101)+(100)+1(100)+1)\)
\((200)+(0(101)+(100)+1(0(101)+(100)(100)+1))\) \((200)+(0(101)+(100)+1(0(101)+(100)(0(101)+(100)(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times \psi_1(\Omega_2^{\Omega+1}))\) |
\((200)+(0(101)+(100)+2(100)+1)\)
|
\((200)+(100)+1\)
\((200)+(0(101)+(100)+1(100)+1)\) \((200)+(0(101)+(100)+1(0(101)+(100)+1(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2)\) |
\((200)+(0(101)+(100)+2(100)+1)+(0(101)+(100)+2(100)+1)\)
|
\((200)+(0(101)+(100)+2(100)+1)+(100)+1\)
\((200)+(0(101)+(100)+2(100)+1)+(0(101)+(100)+1(100)+1)\) \((200)+(0(101)+(100)+2(100)+1)+(0(101)+(100)+1(0(101)+(100)+1(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2))\) |
\((200)+(00(0(101)+(100)+2(100)+1)+1)\)
|
\((200)\)
\((200)+(0(101)+(100)+2(100)+1)\) \((200)+(0(101)+(100)+2(100)+1)+(0(101)+(100)+2(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2) \times \omega)\) |
\((200)+(01(0(101)+(100)+2(100)+1)+1)\)
|
\((200)+(0(101)+(100)+2(100)+1)+1\)
\((200)+(00(0(101)+(100)+2(100)+1)+1)\) \((200)+(00(00(0(101)+(100)+2(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2+\varepsilon_{\Omega+1}))\) |
\((200)+(0\omega(0(101)+(100)+2(100)+1)+1)\)
|
\((200)+(00(0(101)+(100)+2(100)+1)+1)\)
\((200)+(01(0(101)+(100)+2(100)+1)+1)\) \((200)+(02(0(101)+(100)+2(100)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2+\varphi_{\omega}(\Omega+1)))\) |
\((200)+(0(101)+(100)+1(0(101)+(100)+2(100)+1)+1)\)
|
\((200)+(0(101)+(100)+2(100)+1)+1\)
\((200)+(0(101)+(100)(0(101)+(100)+2(100)+1)+1)\) \((200)+(0(101)+(100)(0(101)+(100)(0(101)+(100)+2(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(0)))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega}+\Omega)+1})))\) |
\((200)+(0(101)+(100)+2(100)+2)\)
|
\((200)+(0(101)+(100)+2(100)+1)+1\)
\((200)+(0(101)+(100)+1(0(101)+(100)+2(100)+1)+1)\) \((200)+(0(101)+(100)+1(0(101)+(100)+1(0(101)+(100)+2(100)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)+\psi_2(0))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times 2))\) |
\((200)+(0(101)+(100)+2(100)+\omega)\)
|
\((200)+(100)\)
\((200)+(0(101)+(100)+2(100)+1)\) \((200)+(0(101)+(100)+2(100)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \omega))\) |
\((200)+(0(101)+(100)+2(100)+(100))\)
|
\((200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+1)0))\)
\((200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+1)0))0))\) \((200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+(0(200)+(0(101)+(100)+2(100)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \Omega))\) |
\((200)+(0(101)+(100)+2(00(100)+1)\)
|
\((200)+(0(101)+(100)+20)\)
\((200)+(100)\) \((200)+(0(101)+(100)+2(100)+(100))\) \((200)+(0(101)+(100)+2(100)+(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \Omega^{\omega}))\) |
\((200)+(0(101)+(100)+2(01(100)+1)\)
|
\((200)+(0(101)+(100)+2(100)+1)\)
\((200)+(0(101)+(100)+2(00(100)+1))\) \((200)+(0(101)+(100)+2(00(00(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \varepsilon_{\Omega+1}))\) |
\((200)+(0(101)+(100)+2(0\omega(100)+1)\)
|
\((200)+(0(101)+(100)+2(00(100)+1))\)
\((200)+(0(101)+(100)+2(01(100)+1))\) \((200)+(0(101)+(100)+2(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \varphi_{\omega}(\Omega+1)))\) |
\((200)+(0(101)+(100)+2(0(101)+(100)+2(100)+1)\)
|
\((200)+(0(101)+(100)+2(100)+1)\)
\((200)+(0(101)+(100)+2(0(0(101)+(100)+1(100)+1))\) \((200)+(0(101)+(100)+2(0(0(101)+(100)+1(0(101)+(100)+1(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2+\psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \varphi_{\omega}(\Omega+1)))\) |
\((200)+(0(101)+(100)+3(100)+1)\)
|
\((200)+(100)+1\)
\((200)+(0(101)+(100)+2(100)+1)\) \((200)+(0(101)+(100)+2(0(101)+(100)+2(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{2})\) |
\((200)+(0(101)+(100)+\omega(100)+1)\)
|
\((200)+(0(101)+(100)(100)+1)\)
\((200)+(0(101)+(100)+1(100)+1)\) \((200)+(0(101)+(100)+2(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\omega})\) |
\((200)+(0(101)+(100)+(100)(100)+1)\)
|
\((200)+(0(101)+(100)+(0(101)+(100)+10)(100)+1)\)
\((200)+(0(101)+(100)+(0(101)+(100)+(0(101)+(100)+10)0)(100)+1)\) \((200)+(0(101)+(100)+(0(101)+(100)+(0(101)+(100)+(0(101)+(100)+10)0)0)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(0)+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega}+\Omega \times 2)})\) |
\((200)+(0(101)+(00(100)+1)(100)+1)\)
|
\((200)+(0(101)(100)+1)\)
\((200)+(0(101)+(100)(100)+1)\) \((200)+(0(101)+(100)+(100)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega}+\Omega \times \omega)})\) |
\((200)+(0(101)+(101)(100)+1)\)
|
\((200)+(0(101)+(0(100)(100)+1)(100)+1)\)
\((200)+(0(101)+(0(0(100)(100)+1)(100)+1)(100)+1)\) \((200)+(0(101)+(0(0(0(100)(100)+1)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega}+\Omega \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})}))})\) |
\((200)+(0(00(101)+1)(100)+1)\)
|
\((200)+(00(100)+1)\)
\((200)+(0(101)(100)+1)\) \((200)+(101)+(101)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))))))+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega}+\Omega \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega})})^{\omega})})\) |
\((200)+(0(102)(100)+1)\)
|
\((200)+(0(0(101)(101)+1)(100)+1)\)
\((200)+(0(0(0(101)(101)+1)(101)+1)(100)+1)\) \((200)+(0(0(0(101)(101)+1)(101)+1)(101)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega} \times 2)})\) |
\((200)+(0(200)(100)+1)\)
|
\((200)+(00(100)+1)\)
\((200)+(0(100)(100)+1)\) \((200)+(10(100))+(101)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega^{\Omega+1})})\) |
\((200)+(101)\)
|
\((200)+(0(200)(100)+1)\)
\((200)+(0(200)+(0(200)(100)+1)(100)+1)\) \((200)+(0(200)+(0(200)+(0(200)(100)+1)(100)+1)(100)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega})\) |
\((200)+(102)\)
|
\((200)+(0(200)(101)+1)\)
\((200)+(0(200)+(0(200)(101)+1)(101)+1)\) \((200)+(0(200)+(0(200)+(0(200)(101)+1)(101)+1)(101)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times 2)\) |
\((200)+(10\omega)\)
|
\((200)+(100)\)
\((200)+(101)\) \((200)+(102)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \omega)\) |
\((200)+(10(100))\)
|
\((200)+(10(0(200)+(101)0))\)
\((200)+(10(0(200)+(10(0(200)+(101)0))0))\) \((200)+(10(0(200)+(10(0(200)+(10(0(200)+(101)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \Omega)\) |
\((200)+(10(00(100)+1))\)
|
\((200)+(100)\)
\((200)+(10(100))\) \((200)+(10(100)+(100))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \Omega \times \omega)\) |
\((200)+(10(00(00(100)+1)))\)
|
\((200)+(10(000))\)
\((200)+(10(100))\) \((200)+(10(00(100)+(100)))\) \((200)+(10(00(100)+(100)+(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \Omega^{\omega})\) |
\((200)+(10(01(100)+1))\)
|
\((200)+(100)+1\)
\((200)+(10(00(100)+1))\) \((200)+(10(00(00(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \varepsilon_{\Omega+1})\) |
\((200)+(10(0\omega(100)+1))\)
|
\((200)+(10(00(100)+1))\)
\((200)+(10(01(100)+1))\) \((200)+(10(02(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \varphi_{\omega}(\Omega+1))\) |
\((200)+(10(0(200)(100)+1))\)
|
\((200)+(10(00(100)+1))\)
\((200)+(10(0(100)(100)+1))\) \((200)+(10(0(10(100))(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}))\) |
\((200)+(10(101))\)
|
\((200)+(10(0(200)(100)+1))\)
\((200)+(10(0(200)+(10(0(200)(100)+1))(100)+1))\) \((200)+(10(0(200)+(10(0(200)+(10(0(200)(100)+1))(100)+1))(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega}))\) |
\((200)+(10(102))\)
|
\((200)+(10(0(200)(101)+1))\)
\((200)+(10(0(200)+(10(0(200)(101)+1))(101)+1))\) \((200)+(10(0(200)+(10(0(200)+(10(0(200)(101)+1))(101)+1))(101)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times 2))\) |
\((200)+(10(10\omega))\)
|
\((200)+(10(100))\)
\((200)+(10(101))\) \((200)+(10(102))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \omega))\) |
\((200)+(10(10(100)))\)
|
\((200)+(10(0(200)+(101)0))\)
\((200)+(10(0(200)+(10(0(200)+(101)0))0))\) \((200)+(10(0(200)+(10(0(200)+(10(0(200)+(101)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega} \times \Omega))\) |
\((200)+(110)\)
|
\((200)\)
\((200)+(100)\) \((200)+(10(100))\) \((200)+(10(10(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}))\) |
\((200)+(10(110)+1)\)
|
\((200)+(0(200)(110)+1)\)
\((200)+(0(200)+(0(200)(110)+1)(110)+1)\) \((200)+(0(200)+(0(200)+(0(200)(110)+1)(110)+1)(110)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_2(\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega+1})+1))\) |
\((200)+(10(110)+\omega)\)
|
\((200)+(110)\)
\((200)+(10(110)+1)\) \((200)+(10(110)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times (\psi_1(\Omega_2^{\Omega+1})+\omega))\) |
\((200)+(10(110)+(110))\)
|
\((200)+(110)\)
\((200)+(10(110)+(100))\) \((200)+(10(110)+(10(100)))\) \((200)+(10(110)+(10(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}) \times 2)\) |
\((200)+(10(00(110)+1))\)
|
\((200)+(100)\)
\((200)+(110)\) \((200)+(10(110)+(110))\) \((200)+(10(110)+(110)+(110))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}) \times \omega)\) |
\((200)+(10(01(110)+1))\)
|
\((200)+(10(110)+1)\)
\((200)+(10(00(110)+1))\) \((200)+(10(00(00(110)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2))\) |
\((200)+(10(01(110)+\omega))\)
|
\((200)+(110)\)
\((200)+(10(01(110)+1))\) \((200)+(10(01(110)+2))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))psi_2(0))+\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \omega))\) |
\((200)+(10(01(110)+(110)))\)
|
\((200)+(110)\)
\((200)+(10(01(110)+(100)))\) \((200)+(10(01(110)+(10(100))))\) \((200)+(10(01(110)+(10(10(100)))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \psi_1(\Omega_2^{\Omega+1})))\) |
\((200)+(10(01(00(110)+1)))\)
|
\((200)+(10(010))\)
\((200)+(110)\) \((200)+(10(01(110)+(100)))\) \((200)+(10(01(110)+(110)+(110)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \psi_1(\Omega_2^{\Omega+1}) \times \omega))\) |
\((200)+(10(01(00(00(110)+1))))\)
|
\((200)+(10(01(000)))\)
\((200)+(110)\) \((200)+(10(01(00(110)+(100))))\) \((200)+(10(01(00(110)+(110)+(110))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\pi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \psi_1(\Omega_2^{\Omega+1}+\psi_1(\Omega_2^{\Omega+1}) \times \omega)))\) |
\((200)+(10(01(01(110)+1)))\)
|
\((200)+(10(01(000)))\)
\((200)+(110)\) \((200)+(10(01(00(110)+(100))))\) \((200)+(10(01(00(110)+(110)+(110))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2 \times \psi_1(\Omega_2^{\Omega+1}+\Omega)))\) |
\((200)+(10(02(110)+1))\)
|
\((200)+(10(110)+1)\)
\((200)+(10(01(110)+1))\) \((200)+(10(01(01(110)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{2}))\) |
\((200)+(10(0\omega(110)+1))\)
|
\((200)+(10(00(110)+1))\)
\((200)+(10(01(110)+1))\) \((200)+(10(02(110)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\omega}))\) |
\((200)+(10(0(200)(110)+1))\)
|
\((200)+(10(00(110)+1))\)
\((200)+(10(0(100)(110)+1))\) \((200)+(10(0(10(100))(110)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}))\) |
\((200)+(10(10(110)+1))\)
|
\((200)+(10(0(200)(110)+1))\)
\((200)+(10(0(200)+(10(0(200)(110)+1))(110)+1))\) \((200)+(10(0(200)+(10(0(200)+(10(0(200)(110)+1))(110)+1))(110)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}))}))\) |
\((200)+(111)\)
|
\((200)+(110)+1\)
\((200)+(10(110)+1)\) \((200)+(10(10(110)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\Omega}))\) |
\((200)+(112)\)
|
\((200)+(111)+1\)
\((200)+(10(111)+1)\) \((200)+(10(10(111)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0)))+\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times 2))\) |
\((200)+(11\omega)\)
|
\((200)+(110)\)
\((200)+(111)\) \((200)+(112)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \omega))\) |
\((200)+(11(110))\)
|
\((200)+(110)\)
\((200)+(11(100))\) \((200)+(11(10(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega+1})))\) |
\((200)+(200)\)
|
\((200)\)
\((200)+(110)\) \((200)+(11(110))\) \((200)+(11(11(110)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times 2)\) |
\((00(200)+1)\)
|
\(0\)
\((200)\) \((200)+(200)\) \((200)+(200)+(200)\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \omega)\) |
\((00(200)+(100))\)
|
\((00(200)+(0(00(200)+1)0))\)
\((00(200)+(0(00(200)+(0(00(200)+1)0))0))\) \((00(200)+(0(00(200)+(0(00(200)+(0(00(200)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(0)))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \Omega)\) |
\((00(200)+(101))\)
|
\((00(200)+(0(200)(100)+1))\)
\((00(200)+(0(00(200)+(0(200)(100)+1))(100)+1))\) \((00(200)+(0(00(200)+(0(00(200)+(0(200)(100)+1))(100)+1))(100)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega}))\) |
\((00(200)+(102))\)
|
\((00(200)+(0(200)(101)+1))\)
\((00(200)+(0(00(200)+(0(200)(101)+1))(101)+1))\) \((00(200)+(0(00(200)+(0(00(200)+(0(200)(101)+1))(101)+1))(101)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0)))+)\psi_2(\psi_2(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega} \times 2))\) |
\((00(200)+(10\omega))\)
|
\((00(200)+(100))\)
\((00(200)+(101))\) \((00(200)+(102))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega} \times \omega))\) |
\((00(200)+(10(100)))\)
|
\((00(200)+(10(0(00(200)+(101))0)))\)
\((00(200)+(10(0(00(200)+(10(0(00(200)+(101))0)))0)))\) \((00(200)+(10(0(00(200)+(10(0(00(200)+(10(0(00(200)+(101))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega} \times \Omega))\) |
\((00(200)+(110))\)
|
\((200)\)
\((00(200)+(100))\) \((00(200)+(10(100)))\) \((00(200)+(10(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1}))\) |
\((00(200)+(111))\)
|
\((00(200)+(110)+1)\)
\((00(200)+(10(110)+1))\) \((00(200)+(10(10(110)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1} \times 2))\) |
\((00(200)+(11\omega))\)
|
\((00(200)+(110))\)
\((00(200)+(111))\) \((00(200)+(112))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1} \times \omega))\) |
\((00(200)+(11(100)))\)
|
\((00(200)+(11(0(00(200)+(111))0)))\)
\((00(200)+(11(0(00(200)+(11(0(00(200)+(111))0)))0)))\) \((00(200)+(11(0(00(200)+(11(0(00(200)+(11(0(00(200)+(111))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1} \times \Omega))\) |
\((00(200)+(11(110)))\)
|
\((00(200)+(110))\)
\((00(200)+(11(100)))\) \((00(200)+(11(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1} \times \psi_1(\Omega_2^{\Omega+1})))\) |
\((00(200)+(120))\)
|
\((200)\)
\((00(200)+(110))\) \((00(200)+(11(110)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega+2})\) |
\((00(200)+(1{\omega}0))\)
|
\((00(200)+(100))\)
\((00(200)+(110))\) \((00(200)+(120))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega+\omega})\) |
\((00(200)+(1(100)0))\)
|
\((00(200)+(100)\)
\((00(200)+(110))\) \((00(200)+(1(010)0))\) \((00(200)+(1(0(010)0)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega+\Gamma_0})\) |
\((00(200)+(1(1(100)0)0))\)
|
\((00(200)+(1(100)0))\)
\((00(200)+(1(110)0))\) \((00(200)+(1(1(010)0)0))\) \((00(200)+(1(1(0(010)0)0)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega+\psi_0(\Omega_2^{\Omega+1} \times \Omega)})\) |
\((00(200)+(1(1(1(100)0)0)0))\)
|
\((00(200)+(1(1(100)0)0))\)
\((00(200)+(1(1(110)0)0))\) \((00(200)+(1(1(1(010)0)0)0))\) \((00(200)+(1(1(1(0(010)0)0)0)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega+\psi_0(\Omega_2^{\Omega+\Gamma_0})})\) |
\((00(200)+(200))\)
|
\((00(200)+(100))\)
\((00(200)+(1(100)0))\) \((00(200)+(1(1(100)0)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega \times 2})\) |
\((00(00(200)+1))\)
|
\((000)\)
\((200)\) \((00(200)+(200))\) \((00(200)+(200)+(200))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega \times \omega})\) |
\((00(00(200)+(100)))\)
|
\((00(00(200)+(0(00(00(200)+1))0)))\)
\((00(00(200)+(0(00(00(200)+(0(00(00(200)+1))0)))0)))\) \((00(00(200)+(0(00(00(200)+(0(00(00(200)+(0(00(00(200)+1))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(0)+\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega^{2}})\) |
\((00(00(200)+(00(100)+1)))\)
|
\((200)\)
\((00(00(200)+(100)))\) \((00(00(200)+(100)+(100)))\) \((00(00(200)+(100)+(100)+(100)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega^{\omega}})\) |
\((00(00(200)+(01(100)+1)))\)
|
\((00(00(200)+(100)+1))\)
\((00(00(200)+(00(100)+1)))\) \((00(00(200)+(00(00(100)+1))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\varepsilon_{\Omega+1}})\) |
\((00(00(200)+(110))\)
|
\((200)\)
\((00(00(200)+(100)))\) \((00(00(200)+(10(100))))\) \((00(00(200)+(10(10(100)))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega+1})})\) |
\((00(00(200)+(120))\)
|
\((200)\)
\((00(00(200)+(110)))\) \((00(00(200)+(11(110))))\) \((00(00(200)+(11(11(110)))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega+2})})\) |
\((00(00(200)+(1{\omega}0))\)
|
\((00(00(200)+(100)))\)
\((00(00(200)+(110)))\) \((00(00(200)+(120)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega+\omega})})\) |
\((00(00(200)+(1(100)0))\)
|
\((00(00(200)+(100)))\)
\((00(00(200)+(110)))\) \((00(00(200)+(1(010)0)))\) \((00(00(200)+(1(0(010)0)0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_1(\psi_1(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega+\Gamma_0})})\) |
\((00(00(200)+(1(200)0))\)
|
\((00(00(200)+(1(100)0)))\)
\((00(00(200)+(1(1(100)0)0)))\) \((00(00(200)+(1(1(1(100)0)0)0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega+\psi_0(\Omega_2^{\Omega \times 2})})})\) |
\((00(00(200)+(200)))\)
|
\((00(00(200)+(1(00(00(200)+1))0)))\)
\((00(00(200)+(1(00(00(200)+(1(00(00(200)+1))0)))0)))\) \((00(00(200)+(1(00(00(200)+(1(00(00(200)+(1(00(00(200)+1))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega \times 2})})\) |
\((00(00(00(200)+1))\)
|
\((00(000))\)
\((200)\) \((00(00(200)+(200)))\) \((00(00(200)+(200)+(200)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0)+\psi_0(0)))))))\)
\(= \psi_0(\Omega_2^{\psi_1(\Omega_2^{\Omega \times \omega})})\) |
\((01(200)+1)\)
|
\((200)+1\)
\((00(200)+1)\) \((00(00(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2})\) |
\((01(200)+2)\)
|
\((01(200)+1)+1\)
\((00(01(200)+1)+1)\) \((00(00(01(200)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(0))+\psi_2(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2 \times 2})\) |
\((01(200)+\omega)\)
|
\((200)\)
\((01(200)+1)\) \((01(200)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(0)+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2 \times \omega})\) |
\((01(200)+(100))\)
|
\((01(200)+(0(01(200)+1)0))\)
\((01(200)+(0(01(200)+(0(01(200)+1)0))0))\) \((01(200)+(0(01(200)+(0(01(200)+(0(01(200)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(0)+\psi_1(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2 \times \Omega})\) |
\((01(200)+(200))\)
|
\((01(200)+(100))\)
\((01(200)+(1(100)0))\) \((01(200)+(1(1(100)0)0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(0)+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{2}})\) |
\((01(00(200)+1))\)
|
\((200)\)
\((01(200)+(200))\) \((01(200)+(200)+(200))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\omega}})\) |
\((01(00(200)+(100)))\)
|
\((01(200)+(0(01(200)+1)0))\)
\((01(200)+(0(01(200)+(0(01(200)+1)0))0))\) \((01(200)+(0(01(200)+(0(01(200)+(0(01(200)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega}})\) |
\((01(00(200)+(101)))\)
|
\((01(200)+(0(01(200)+1)(100)+1))\)
\((01(200)+(0(01(200)+(0(01(200)+1)(100)+1))(100)+1))\) \((01(200)+(0(01(200)+(0(01(200)+(0(01(200)+1)(100)+1))(100)+1))(100)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\psi_1(\Omega_2^{\Omega})}})\) |
\((01(00(200)+(110)))\)
|
\((200)\)
\((01(200)+(100))\) \((01(200)+(10(100)))\) \((01(200)+(10(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\psi_1(\Omega_2^{\Omega+1})}})\) |
\((01(00(200)+(200)))\)
|
\((01(00(200)+(1(01(00(200)+1))0)))\)
\((01(00(200)+(1(01(00(200)+(1(01(00(200)+1))0)))0)))\) \((01(00(200)+(1(01(00(200)+(1(01(00(200)+(1(01(00(200)+(1(01(00(200)+1))0)))0)))0)))0)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\psi_1(\Omega_2^{\Omega \times 2})}})\) |
\((01(00(00(200)+1)))\)
|
\((200)\)
\((01(00(200)+(200)))\) \((01(00(200)+(200)+(200)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_1(0)+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\psi_1(\Omega_2^{\Omega \times \omega})}})\) |
\((01(01(200)+1))\)
|
\((01(200)+1)\)
\((01(00(200)+1))\) \((01(00(00(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\psi_1(\Omega_2^{\Omega_2})}})\) |
\((02(200)+1)\)
|
\((200)+1\)
\((01(200)+1)\) \((01(01(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2}})\) |
\((0\omega(200)+1)\)
|
\((00(200)+1)\)
\((01(200)+1)\) \((02(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\omega}}})\) |
\((0(200)(200)+1)\)
|
\((00(200)+1)\)
\((0(100)(200)+1)\) \((0(10(100))(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}}})\) |
\((0(0(200)(200)+1)(200)+1)\)
|
\((0(00(200)+1)(200)+1)\)
\((0(0(100)(200)+1)(200)+1)\) \((0(0(10(100))(200)+1)(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}}})}}})\) |
\((10(200)+1)\)
|
\((0(200)(200)+1)\)
\((0(0(200)(200)+1)(200)+1)\) \((0(0(0(200)(200)+1)(200)+1)(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})\) |
\((10(200)+1)+(200)\)
|
\((10(200)+1)+(1(10(200)+1)0)\)
\((10(200)+1)+(1(10(200)+1)+(1(10(200)+1)0)0)\) \((10(200)+1)+(1(10(200)+1)+(1(10(200)+1)+(1(10(200)+1)0)0)0)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega+1})\) |
\((10(200)+1)+(00(200)+1)\)
|
\((10(200)+1)\)
\((10(200)+1)+(200)\) \((10(200)+1)+(200)+(200)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega+1} \times \omega)\) |
\((10(200)+1)+(01(200)+1)\)
|
\((10(200)+1)+(200)+1\)
\((10(200)+1)+(00(200)+1)\) \((10(200)+1)+(00(00(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega_2})\) |
\((10(200)+1)+(02(200)+1)\)
|
\((10(200)+1)+(200)+1\)
\((10(200)+1)+(01(200)+1)\) \((10(200)+1)+(01(01(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega_2^{\Omega_2}})\) |
\((10(200)+1)+(0\omega(200)+1)\)
|
\((10(200)+1)+(00(200)+1)\)
\((10(200)+1)+(01(200)+1)\) \((10(200)+1)+(02(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega_2^{\Omega_2^{\omega}}})\) |
\((10(200)+1)+(0(200)(200)+1)\)
|
\((10(200)+1)+(00(200)+1)\)
\((10(200)+1)+(0(100)(200)+1)\) \((10(200)+1)+(0(10(100))(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega_2^{\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}}})\) |
\((10(200)+1)+(0(10(200)+1)(200)+1)\)
|
\((10(200)+1)+(0(0(200)(200)+1)(200)+1)\)
\((10(200)+1)+(0(0(0(200)(200)+1)(200)+1)(200)+1)\) \((10(200)+1)+(0(0(0(0(200)(200)+1)(200)+1)(200)+1)(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega_2^{\Omega_2^{\psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})}}})\) |
\((10(200)+1)+(10(200)+1)\)
|
\((10(200)+1)+(0(10(200)+1)(200)+1)\)
\((10(200)+1)+(0(10(200)+1)+(0(10(200)+1)(200)+1)(200)+1)\) \((10(200)+1)+(0(10(200)+1)+(0(10(200)+1)+(0(10(200)+1)(200)+1)(200)+1)(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times 2)\) |
\((00(10(200)+1)+1)\)
|
\(0\)
\((10(200)+1)\) \((10(200)+1)+(10(200)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_0(0)))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \omega)\) |
\((00(10(200)+1)+(110))\)
|
\((10(200)+1)\)
\((00(10(200)+1)+(100))\) \((00(10(200)+1)+(10(100)))\) \((00(10(200)+1)+(10(10(100))))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega+1}))\) |
\((00(10(200)+1)+(200))\)
|
\((00(10(200)+1)+(1(00(10(200)+1)+1)0))\)
\((00(10(200)+1)+(1(00(10(200)+1)+(1(00(10(200)+1)+1)0))0))\) \((00(10(200)+1)+(1(00(10(200)+1)+(1(00(10(200)+1)+(1(00(10(200)+1)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega \times 2}))\) |
\((00(10(200)+1)+(00(200)+1))\)
|
\((10(200)+1)\)
\((00(10(200)+1)+(200))\) \((00(10(200)+1)+(200)+(200))\) \((00(10(200)+1)+(200)+(200)+(200))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_1(0)+\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega \times \omega}))\) |
\((00(10(200)+1)+(01(200)+1))\)
|
\((00(10(200)+1)+(200)+1)\)
\((00(10(200)+1)+(00(200)+1))\) \((00(10(200)+1)+(00(00(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2}))\) |
\((00(10(200)+1)+(02(200)+1))\)
|
\((00(10(200)+1)+(200)+1)\)
\((00(10(200)+1)+(01(200)+1))\) \((00(10(200)+1)+(01(01(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(0)))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2}}))\) |
\((00(10(200)+1)+(0\omega(200)+1))\)
|
\((00(10(200)+1)+(00(200)+1))\)
\((00(10(200)+1)+(01(200)+1))\) \((00(10(200)+1)+(02(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\omega}}}))\) |
\((00(10(200)+1)+(10(200)+1))\)
|
\((00(10(200)+1)+(0(00(10(200)+1)+1)(200)+1))\)
\((00(10(200)+1)+(0(00(10(200)+1)+(0(00(10(200)+1)+1)(200)+1))(200)+1))\) \((00(10(200)+1)+(0(00(10(200)+1)+(0(00(10(200)+1)+(0(00(10(200)+1)+1)(200)+1))(200)+1))(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})})\) |
\((00(00(10(200)+1)+1))\)
|
\((000)\)
\((10(200)+1)\) \((00(10(200)+1)+(10(200)+1))\) \((00(10(200)+1)+(10(200)+1)+(10(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_0(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})^{\omega})\) |
\((00(00(00(10(200)+1)+1)))\)
|
\((00(000))\)
\((10(200)+1)\) \((00(00(10(200)+1)+(10(200)+1)))\) \((00(00(10(200)+1)+(10(200)+1)+(10(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})))\) |
\((01(10(200)+1)+1)\)
|
\((10(200)+1)+1\)
\((00(10(200)+1)+1)\) \((00(00(10(200)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(0))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2))\) |
\((02(10(200)+1)+1)\)
|
\((10(200)+1)+1\)
\((01(10(200)+1)+1)\) \((01(01(10(200)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{2}))\) |
\((0\omega(10(200)+1)+1)\)
|
\((00(10(200)+1)+1)\)
\((01(10(200)+1)+1)\) \((02(10(200)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_0(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\omega}))\) |
\((0(200)(10(200)+1)+1)\)
|
\((00(10(200)+1)+1)\)
\((0(100)(10(200)+1)+1)\) \((0(10(100))(10(200)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_1(0))+\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\psi_0(\Omega_2^{\Omega+1})}))\) |
\((0(10(200)+1)(10(200)+1)+1)\)
|
\((0(0(200)(200)+1)(10(200)+1)+1)\)
\((0(0(0(200)(200)+1)(200)+1)(10(200)+1)+1)\) \((0(0(0(0(200)(200)+1)(200)+1)(200)+1)(10(200)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})}))\) |
\((10(200)+2)\)
|
\((0(10(200)+1)(10(200)+1)+1)\)
\((0(0(10(200)+1)(10(200)+1)+1)(10(200)+1)+1)\) \((0(0(0(10(200)+1)(10(200)+1)+1)(10(200)+1)+1)(10(200)+1)+1)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega}))\) |
\((10(200)+\omega)\)
|
\((200)\)
\((10(200)+1)\) \((10(200)+2)\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \omega))\) |
\((10(200)+(200))\)
|
\((10(200)+(1(10(200)+1)0))\)
\((10(200)+(1(10(200)+(1(10(200)+1)0))0))\) \((10(200)+(1(10(200)+(1(10(200)+(1(10(200)+1)0))0))0))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0))+\psi_2(\psi_1(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega \times 2})))\) |
\((10(00(200)+1))\)
|
\((100)\)
\((200)\) \((10(200)+(200))\) \((10(200)+(200)+(200))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_1(0)+\psi_0(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega \times \omega})))\) |
\((10(01(200)+1))\)
|
\((10(200)+1)\)
\((10(00(200)+1))\) \((10(00(00(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_2(0))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega_2})))\) |
\((10(02(200)+1))\)
|
\((10(200)+1)\)
\((10(01(200)+1))\) \((10(01(01(200)+1)))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(0)))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2}})))\) |
\((10(0\omega(200)+1))\)
|
\((10(00(200)+1))\)
\((10(01(200)+1))\) \((10(02(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_0(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\omega}}})))\) |
\((10(10(200)+1))\)
|
\((10(0(200)(200)+1))\)
\((10(0(10(0(200)(200)+1))(200)+1))\) \((10(0(10(0(10(0(200)(200)+1))(200)+1))(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))))))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}})))\) |
\((11(200)+1)\)
|
\((200)+1\)
\((10(200)+1)\) \((10(10(200)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega+1}))\) |
\((11(200)+2)\)
|
\((11(200)+1)+1\)
\((10(11(200)+1)+1)\) \((10(10(11(200)+1)+1))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega+1} \times 2))\) |
\((11(200)+\omega)\)
|
\((200)\)
\((11(200)+1)\) \((11(200)+2))\) |
\(\psi_0(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0))))+\psi_1(\psi_2(\psi_2(\psi_2(\psi_2(\psi_1(0)))))+\psi_2(\psi_2(\psi_1(0))+\psi_2(0)+\psi_0(0)))))\)
\(= \psi_0(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}} \times \psi_1(\Omega_2^{\Omega_2^{\Omega_2^{\Omega}}}+\Omega_2^{\Omega+1} \times \omega))\) |
WIP
Up to BO[]
I describe the ordinal types into normal forms for Buchholz's function. I think that this is just a poem rather than a table of expectation.
WIP
Up to \(\psi_{0}(\Omega_{\Omega_{\cdot_{\cdot_{\cdot_{\Omega}}}}})\)[]
I describe the ordinal types into normal forms for extended Buchholz's function.
WIP
See Also[]
- The original Japanese blog post
- A source code of the computation of fundamental sequences by rpakr
- An analysis by rpakr