\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{t29\_rewrite3 (TMHzH2Q36iCk4KP9zVfMUaMNpS7sKszkUNB)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_rewrite3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X0){\unicdcdcdid}((v2\_xxreal\_0~X1){\unicdcdcdid}(v3\_xxreal\_0~X0)))))\end{array}
\label{hyp:ehgdpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k8\_afinsq\_1~X3))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (l1\_rewrite3~X5~X4){\unicdbdjdcd}(\preoh (\preoh k2\_flang\_1~X3 \in k10\_xtuple\_0~\\
(k9\_xtuple\_0~(u1\_rewrite3~X4~X5))){\unicdcdcdhd}(r2\_rewrite3~X3~X4~X5~X0~X1~X2~\\
X1))))\end{array}
\label{hyp:ehcdidpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (l1\_rewrite3~X6~X5){\unicdbdjdcd}(\preoh (r2\_rewrite3~\\
X2~X5~X6~X0~X3~X1~X4){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(k8\_afinsq\_1~X2)){\unicdbdjdcd}\\
(\preoh (r1\_rewrite3~X5~X6~X0~X7~X1){\unicdcdcdhd}(X3=k1\_flang\_1~X2~X7~X4))))))))\end{array}
\label{hyp:ehcdcdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (l1\_rewrite3~\\
X4~X0){\unicdbdjdcd}((r1\_rewrite3~X0~X4~X1~X2~X3){\unicdbdjdcd}((r1\_struct\_0~X4~X1){\unicdcdcdhd}((X2 \in \\
X0){\unicdcdcdhd}((r1\_struct\_0~X4~X3){\unicdcdcdhd}((X1 \in k9\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~\\
X0~X4))){\unicdcdcdhd}((X2 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~X0~X4))){\unicdcdcdhd}\\
(X3 \in k10\_xtuple\_0~(u1\_rewrite3~X0~X4))))))))\end{array}
\label{hyp:ehbdfdpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k8\_afinsq\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k8\_afinsq\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((X1=k1\_flang\_1~X0~X2~X3){\unicdbdjdcd}(\\
(X2=k2\_flang\_1~X0){\unicdcdcdid}((X3=k2\_flang\_1~X0){\unicdcdcdid}((\preoh r1\_xxreal\_0~(k1\_afinsq\_1~\\
X1)~(k1\_afinsq\_1~X2)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k1\_afinsq\_1~X1)~(k1\_afinsq\_1~\\
X3)))))))))\end{array}
\label{hyp:ehbdadpfchfghhchjgehfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_flang\_1}~{X0}}={{k4\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k1\_afinsq\_1~X0=k1\_card\_1~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}((v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k4\_afinsq\_1~X0)){\unicdcdcdhd}((v5\_relat\_1~(k4\_afinsq\_1~\\
X0)~X0){\unicdcdcdhd}((v5\_ordinal1~(k4\_afinsq\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_afinsq\_1~\\
X0)){\unicdcdcdhd}((v1\_xboole\_0~(k4\_afinsq\_1~X0)){\unicdcdcdhd}(v1\_finset\_1~(k4\_afinsq\_1~\\
X0))))))\end{array}
\label{hyp:ggdgedpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_card\_1~X0)){\unicdcdcdhd}\\
(v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgcdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v4\_funct\_1}~{({{k8\_afinsq\_1}~{X0}})}}}\label{hyp:ggdgcdedpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_xboole\_0~(k1\_card\_1~X0)){\unicdcdcdhd}(\\
v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_funct\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)))\end{array}
\label{hyp:dgdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v1\_finset\_1}~{X0}})}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v7\_ordinal1}~{X0}})}{\unicdcdcdhd}{({\preoh{{{v3\_xxreal\_0}~{X0}}}})}})}}}\label{hyp:dgdgddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k8\_afinsq\_1~X0)){\unicdbdjdcd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgbdadpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfchfghhchjgehfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(k8\_afinsq\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~(\\
k8\_afinsq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X6 .  (l1\_rewrite3~X6~X5){\unicdbdjdcd}(\preoh (\preoh k2\_flang\_1~\\
X2 \in k10\_xtuple\_0~(k9\_xtuple\_0~(u1\_rewrite3~X5~X6))){\unicdcdcdhd}((r2\_rewrite3~\\
X2~X5~X6~X0~X3~X1~X4){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_afinsq\_1~X3)~(k1\_afinsq\_1~\\
X4))))))))\end{array}$$
\end{theorem}
\end{document}
