\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{t12\_matrix\_2 (TMcypnvwqtfJ58qcAorhUPYgWGVjmtzbGgo)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}((k4\_matrix\_1~X0~X1=k4\_matrix\_1~\\
X0~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_matrix\_1~X1)~k6\_numbers){\unicdcdcdid}((r1\_xxreal\_0~\\
(k1\_matrix\_1~X2)~k6\_numbers){\unicdcdcdid}(X1=X2))))))\end{array}
\label{hyp:ehbdbdpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfngbgehchjgihpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~(k1\_matrix\_1~\\
X1)~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_matrix\_1~X2)~k6\_numbers){\unicdcdcdhd}\\
(\preoh (X1=X2){\unicdbdjded}((k4\_matrix\_1~X0~X1=k4\_matrix\_1~X0~X2){\unicdcdcdhd}(k1\_matrix\_1~\\
X1=k1\_matrix\_1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
