\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{t83\_abcmiz\_0 (TMGgQTsYAvAzbzB7arCfzW1JUYRWmLte5VQ)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v14\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rewrite1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_rewrite1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_abcmiz\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_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.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}\\
((v9\_abcmiz\_0~X0){\unicdcdcdhd}((v14\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~X0))))))))){\unicdbdjdcd}\\
((v8\_rewrite1~(k11\_abcmiz\_0~X0)){\unicdcdcdhd}(v4\_rewrite1~(k11\_abcmiz\_0~\\
X0)))\end{array}
\label{hyp:ehhdhdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}\\
((v9\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~X0)))))))){\unicdbdjdcd}(v3\_rewrite1~(k11\_abcmiz\_0~\\
X0))\end{array}
\label{hyp:ehgdjdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_rewrite1~X0){\unicdcdcdhd}(v4\_rewrite1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r2\_rewrite1~X0~X1~X2){\unicdbdjdcd}(k2\_rewrite1~\\
X0~X1=k2\_rewrite1~X0~X2))\end{array}
\label{hyp:ehfdfdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_rewrite1~\\
X0~X1~X2){\unicdbdjdcd}((r2\_rewrite1~X0~X1~X2){\unicdcdcdhd}(r2\_rewrite1~X0~X2~X1)))\end{array}
\label{hyp:ehcdfdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}((v9\_abcmiz\_0~X0){\unicdcdcdhd}\\
(l2\_abcmiz\_0~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_abcmiz\_0~X0)){\unicdbdjdcd}((X2 \in k2\_abcmiz\_0~\\
X0~X1){\unicdbdjdcd}((r1\_abcmiz\_0~X0~X1~X2){\unicdcdcdhd}(k5\_abcmiz\_0~X0~X1~X2=X1)))))\end{array}
\label{hyp:ehcdedpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k4\_tarski~\\
X1~X2 \in X0){\unicdbdjdcd}(r1\_rewrite1~X0~X1~X2))\end{array}
\label{hyp:ehbdfdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_abcmiz\_0}~{X0}})}{\unicdbdjdcd}{({{l2\_abcmiz\_0}~{X0}})}}}\label{hyp:egehpfmgddpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}(l2\_abcmiz\_0~X0)))){\unicdcdcdhd}((m1\_subset\_1~X1~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_abcmiz\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k5\_abcmiz\_0~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgfdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~X0))))){\unicdbdjdcd}(m1\_subset\_1~(\\
k11\_abcmiz\_0~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdbdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}\\
((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}((v9\_abcmiz\_0~X0){\unicdcdcdhd}((v14\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k12\_abcmiz\_0~X0~X1=k2\_rewrite1~(k11\_abcmiz\_0~X0)~X1))\end{array}
\label{hyp:egddcdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))){\unicdbdjdcd}\\
((X1=k11\_abcmiz\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_domain\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X2~X3 \in X1){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u1\_abcmiz\_0~X0)){\unicdcdcdhd}((\preoh X4 \in k2\_abcmiz\_0~X0~X3){\unicdcdcdhd}((r4\_abcmiz\_0~\\
X0~X3~X4){\unicdcdcdhd}(k5\_abcmiz\_0~X0~X3~X4=X2)))))))))\end{array}
\label{hyp:egddbdpfbgcgdgngjgkhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_rewrite1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v2\_rewrite1~X0))\end{array}
\label{hyp:dgdgfdpfchfghhchjgehfgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgedpfchfgmgdhfgehpfbd}
\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}
\begin{theorem}\label{thm:ehidddpfbgcgdgngjgkhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v1\_abcmiz\_0~X0){\unicdcdcdhd}\\
((\preoh v4\_abcmiz\_0~X0){\unicdcdcdhd}((v9\_abcmiz\_0~X0){\unicdcdcdhd}((v14\_abcmiz\_0~X0){\unicdcdcdhd}(l3\_abcmiz\_0~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_abcmiz\_0~X0)){\unicdbdjdcd}((r4\_abcmiz\_0~\\
X0~X1~X2){\unicdbdjdcd}(k12\_abcmiz\_0~X0~(k5\_abcmiz\_0~X0~X1~X2)=k12\_abcmiz\_0~\\
X0~X1))))\end{array}$$
\end{theorem}
\end{document}
