\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{t10\_c0sp1 (TMcoSmBkL8wj7zSdsLGxameLvyY2Y1tRbEH)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_c0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_funcsdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funcsdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_c0sp1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v2\_funcsdom~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~X0){\unicdcdcdhd}(\\
l1\_funcsdom~X0)))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v4\_c0sp1~X1~X0){\unicdcdcdhd}(v3\_c0sp1~X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~\\
X1){\unicdcdcdid}(m2\_c0sp1~(g1\_funcsdom~X1~(k2\_c0sp1~X0~X1)~(k1\_c0sp1~X0~X1)~\\
(k5\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))~X0))))\end{array}
\label{hyp:ehgdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v13\_algstr\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}((v3\_group\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_group\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_vectsp\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_vectsp\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}((v7\_rlvect\_1~(k12\_funcsdom~X0)){\unicdcdcdhd}((v1\_funcsdom~(k12\_funcsdom~\\
X0)){\unicdcdcdhd}(v2\_funcsdom~(k12\_funcsdom~X0)))))))))))))\end{array}
\label{hyp:ggdggdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k12\_funcsdom~X0)){\unicdcdcdhd}(v1\_funcsdom~(k12\_funcsdom~\\
X0))\end{array}
\label{hyp:ggdgfdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp1~X0)){\unicdcdcdhd}\\
((v3\_c0sp1~(k6\_c0sp1~X0)~(k12\_funcsdom~X0)){\unicdcdcdhd}(v4\_c0sp1~(k6\_c0sp1~\\
X0)~(k12\_funcsdom~X0))))\end{array}
\label{hyp:ggdgddpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_c0sp1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k6\_c0sp1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~(k12\_funcsdom~\\
X0)))))\end{array}
\label{hyp:egehpflggdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funcsdom~(k12\_funcsdom~X0)){\unicdcdcdhd}(l1\_funcsdom~(k12\_funcsdom~\\
X0))\end{array}
\label{hyp:egehpflgbdcdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(k7\_c0sp1~X0=g1\_funcsdom~(k6\_c0sp1~\\
X0)~(k2\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(k1\_c0sp1~(k12\_funcsdom~\\
X0)~(k6\_c0sp1~X0))~(k5\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(\\
k4\_c0sp1~(k12\_funcsdom~X0)~(k6\_c0sp1~X0))~(k3\_c0sp1~(k12\_funcsdom~\\
X0)~(k6\_c0sp1~X0)))\end{array}
\label{hyp:egbdedpfdgaddhahbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(m2\_c0sp1~(k7\_c0sp1~X0)~(k12\_funcsdom~\\
X0))\end{array}$$
\end{theorem}
\end{document}
