\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{t2\_scmbsort (TMQGLQCh7oUHQEjubRLCBpAgqZ2qrz8ZbNS)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k14\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k18\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_int\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k16\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_scmfsa\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k14\_scmfsa\_2~X1~X2~X0)~X3)~(k4\_struct\_0~k1\_scmfsa\_2)=\\
k4\_card\_1~(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X3)){\unicdcdcdhd}(({\unicdcdaddd} X4 .  (\\
m1\_subset\_1~X4~k5\_numbers){\unicdcdcdhd}((X4=k1\_int\_2~(k1\_funct\_1~X3~X2)){\unicdcdcdhd}\\
(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k14\_scmfsa\_2~X1~X2~\\
X0)~X3)~X1=k7\_partfun1~k4\_numbers~(k18\_scmfsa\_2~X3~X0)~X4))){\unicdcdcdhd}(\\
({\unicdcdadad} X4 .  ((v1\_ami\_2~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
((X4{\unicdcdgdad}X1){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k14\_scmfsa\_2~\\
X1~X2~X0)~X3)~X4=k1\_funct\_1~X3~X4))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_scmfsa\_2~X4){\unicdbdjdcd}\\
(r2\_relset\_1~k5\_numbers~k4\_numbers~(k18\_scmfsa\_2~(k2\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k14\_scmfsa\_2~X1~X2~X0)~X3)~X4)~(k18\_scmfsa\_2~\\
X3~X4)))))))))\end{array}
\label{hyp:ehhdcdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{k1\_int\_2}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k18\_complex1}~{X0}}={{k16\_complex1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdcdcdhd}\\
((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2)))){\unicdbdjdcd}\\
(v1\_int\_1~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdgedpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgddpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhdgngcgdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_scmfsa\_2~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_ami\_2~X2){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~np\_\_3~\\
k1\_scmfsa\_2~(k14\_scmfsa\_2~X3~X2~X1)~X0)~X3=k7\_partfun1~k4\_numbers~\\
(k18\_scmfsa\_2~X0~X1)~(k18\_complex1~(k1\_funct\_1~X0~X2))))))\end{array}$$
\end{theorem}
\end{document}
