\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{t38\_equation (TMQbsLSBckScxEXxrvmMKaA475DqsD2gBRE)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_equation : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_pralg\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ r2\_equation : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k14\_pralg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_equation : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_funct\_1~(k4\_equation~X1)~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_pralg\_2~X4~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X5 .  \preoh (X5 \in X0){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  (l3\_msualg\_1~X6~X1){\unicdbdjdcd}(\preoh (X6=k1\_funct\_1~X4~X5){\unicdcdcdhd}(r1\_equation~\\
X1~X6~X2~X3)))){\unicdbdjdcd}(r1\_equation~X1~(k14\_pralg\_2~X0~X1~X4)~X2~X3)))))\end{array}
\label{hyp:ehddhdpffgbhfhbgehjgpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdcdcdhd}(m1\_pralg\_2~X2~X0~X1)){\unicdbdjdcd}(l3\_msualg\_1~(\\
k14\_pralg\_2~X0~X1~X2)~X1)\end{array}
\label{hyp:egehpflgbdedpfahchbgmghgpfcd}
\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 .  (m3\_pboole~\\
X2~(u1\_struct\_0~X0)~(k4\_equation~X0)){\unicdbdjdcd}((r2\_equation~X0~X1~X2){\unicdbdjded}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_funct\_1~(k4\_equation~X0)~X3)){\unicdbdjdcd}((X4 \in k1\_funct\_1~X2~X3){\unicdbdjdcd}(\\
r1\_equation~X0~X1~X3~X4)))))))\end{array}
\label{hyp:eggdpffgbhfhbgehjgpgog}
\end{equation}
\begin{theorem}\label{thm:ehddidpffgbhfhbgehjgpgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((\preoh v11\_struct\_0~X1){\unicdcdcdhd}\\
(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pboole~X2~(u1\_struct\_0~X1)~\\
(k4\_equation~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pralg\_2~X3~X0~X1){\unicdbdjdcd}(({\unicdcdadad} X4 .  \\
\preoh (X4 \in X0){\unicdcdcdhd}({\unicdcdadad} X5 .  (l3\_msualg\_1~X5~X1){\unicdbdjdcd}(\preoh (X5=k1\_funct\_1~X3~\\
X4){\unicdcdcdhd}(r2\_equation~X1~X5~X2)))){\unicdbdjdcd}(r2\_equation~X1~(k14\_pralg\_2~X0~\\
X1~X3)~X2))))\end{array}$$
\end{theorem}
\end{document}
