\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t22\_msuhom\_1 (TMPUz39jP5SWZxBy781FfyssNMr36HZaer3)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msuhom\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_msuhom\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r3\_alg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r1\_alg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v5\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_msualg\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_msualg\_1~X1~X0){\unicdcdcdhd}((\\
v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}(X1=k1\_msuhom\_1~X0~X0~\\
X1))\end{array}
\label{hyp:ehjdpfngdhfhigpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k1\_funct\_1}~{({{{k16\_funcop\_1}~{X0}}~{X1}})}}~{X0}}={X1}}}}\label{hyp:ehhdcdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_tarski}~{X0}}~{X0}}={{k1\_tarski}~{X0}}}}\label{hyp:ehcdjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((r1\_unialg\_2~\\
X0~X1){\unicdcdcdhd}(r1\_msualg\_3~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)~(k1\_msuhom\_1~\\
(k6\_msualg\_1~X0)~(k6\_msualg\_1~X1)~(k9\_msualg\_1~X1))~(k2\_msuhom\_1~\\
X0~X1~X2))){\unicdbdjdcd}(r1\_alg\_1~X0~X1~X2))))\end{array}
\label{hyp:ehcdbdpfngdhfhigpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}((r1\_unialg\_2~X0~X1){\unicdbdjdcd}(k6\_msualg\_1~\\
X0=k6\_msualg\_1~X1)))\end{array}
\label{hyp:ehbdadpfngdhfhigpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k2\_relset\_1~X0~X1=k10\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0)){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~X0))))){\unicdcdcdhd}(m2\_pboole~\\
X2~(u4\_struct\_0~X0)~(k3\_relat\_1~(u1\_msualg\_1~X0)~(k6\_finseq\_2~\\
(u1\_struct\_0~X0)~X1))~(k3\_relat\_1~(u2\_msualg\_1~X0)~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g3\_msualg\_1~X0~X1~X2=g3\_msualg\_1~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v4\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:ggdgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v13\_struct\_0~\\
(k6\_msualg\_1~X0)~np\_\_1){\unicdcdcdhd}((v1\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v5\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:ggdgcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l3\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:egehpflgjdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(m2\_pboole~(k8\_msualg\_1~\\
X0)~(u4\_struct\_0~(k6\_msualg\_1~X0))~(k3\_relat\_1~(u1\_msualg\_1~(\\
k6\_msualg\_1~X0))~(k6\_finseq\_2~(u1\_struct\_0~(k6\_msualg\_1~X0))~\\
(k7\_msualg\_1~X0)))~(k3\_relat\_1~(u2\_msualg\_1~(k6\_msualg\_1~X0))~\\
(k7\_msualg\_1~X0)))\end{array}
\label{hyp:egehpflgidpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v1\_relat\_1~(k7\_msualg\_1~\\
X0)){\unicdcdcdhd}((v2\_relat\_1~(k7\_msualg\_1~X0)){\unicdcdcdhd}((v4\_relat\_1~(k7\_msualg\_1~\\
X0)~(u1\_struct\_0~(k6\_msualg\_1~X0))){\unicdcdcdhd}((v1\_funct\_1~(k7\_msualg\_1~\\
X0)){\unicdcdcdhd}(v1\_partfun1~(k7\_msualg\_1~X0)~(u1\_struct\_0~(k6\_msualg\_1~\\
X0)))))))\end{array}
\label{hyp:egehpflghdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k6\_msualg\_1~X0)){\unicdcdcdhd}((v5\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l1\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~\\
X0){\unicdcdcdhd}((v3\_unialg\_1~X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((\\
v4\_unialg\_1~X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}(m2\_pboole~\\
(k2\_msuhom\_1~X0~X1~X2)~(u1\_struct\_0~(k6\_msualg\_1~X0))~(u3\_msualg\_1~\\
(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0))~(u3\_msualg\_1~(k6\_msualg\_1~\\
X0)~(k1\_msuhom\_1~(k6\_msualg\_1~X0)~(k6\_msualg\_1~X1)~(k9\_msualg\_1~\\
X1))))\end{array}
\label{hyp:egehpflgcdpfngdhfhigpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(k7\_msualg\_1~X0=\\
k16\_funcop\_1~k6\_numbers~(u1\_struct\_0~X0))\end{array}
\label{hyp:egjdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r2\_msualg\_3~X0~X1~X2~X3){\unicdbdjded}((r1\_msualg\_3~\\
X0~X1~X2~X3){\unicdcdcdhd}(v2\_msualg\_3~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~\\
(u3\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:egidpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v7\_struct\_0~\\
X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_msualg\_1~X1){\unicdcdcdhd}((v5\_msualg\_1~X1){\unicdcdcdhd}\\
(l1\_msualg\_1~X1))))){\unicdbdjdcd}((X1=k6\_msualg\_1~X0){\unicdbdjded}((u1\_struct\_0~X1=\\
k1\_tarski~k6\_numbers){\unicdcdcdhd}((u4\_struct\_0~X1=k4\_finseq\_1~(k1\_unialg\_1~\\
X0)){\unicdcdcdhd}((u1\_msualg\_1~X1=k1\_partfun1~k5\_numbers~k5\_numbers~k5\_numbers~\\
(k3\_finseq\_2~(k1\_tarski~k6\_numbers))~(k1\_unialg\_1~X0)~(k7\_finseq\_2~\\
k6\_numbers)){\unicdcdcdhd}(u2\_msualg\_1~X1=k1\_margrel1~k5\_numbers~(k4\_finseq\_1~\\
(k1\_unialg\_1~X0))~k6\_numbers))))))\end{array}
\label{hyp:egidpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((k6\_msualg\_1~\\
X0=k6\_msualg\_1~X1){\unicdbdjdcd}(k2\_msuhom\_1~X0~X1~X2=k16\_funcop\_1~k6\_numbers~\\
X2))))\end{array}
\label{hyp:egddpfngdhfhigpgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_pboole~X3~X0~X1~X2){\unicdbdjdcd}((v2\_msualg\_3~X3~X0~X1~X2){\unicdbdjded}(\\
{\unicdcdadad} X4 .  (X4 \in X0){\unicdbdjdcd}(k10\_xtuple\_0~(k1\_funct\_1~X3~X4)=k1\_funct\_1~\\
X2~X4)))))\end{array}
\label{hyp:egddpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((r3\_alg\_1~\\
X0~X1~X2){\unicdbdjded}((r1\_alg\_1~X0~X1~X2){\unicdcdcdhd}(k2\_relset\_1~(u1\_struct\_0~X1)~X2=\\
u1\_struct\_0~X1)))))\end{array}
\label{hyp:egddpfbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3=X0){\unicdcdcdid}(X3=X1)))\end{array}
\label{hyp:egcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(k9\_msualg\_1~X0=\\
g3\_msualg\_1~(k6\_msualg\_1~X0)~(k7\_msualg\_1~X0)~(k8\_msualg\_1~X0))\end{array}
\label{hyp:egbdbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v13\_struct\_0~X0~np\_\_1){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(v7\_struct\_0~X0)))\end{array}
\label{hyp:dgdgbdbdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}((v3\_msualg\_1~X1~X0){\unicdbdjdcd}(X1=g3\_msualg\_1~X0~\\
(u3\_msualg\_1~X0~X1)~(u4\_msualg\_1~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfngdhfhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfngdhfhigpgngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(((r1\_unialg\_2~\\
X0~X1){\unicdcdcdhd}(r2\_msualg\_3~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)~(k1\_msuhom\_1~\\
(k6\_msualg\_1~X0)~(k6\_msualg\_1~X1)~(k9\_msualg\_1~X1))~(k2\_msuhom\_1~\\
X0~X1~X2))){\unicdbdjdcd}(r3\_alg\_1~X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
