\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\_scpisort (TMNrQ1aWPHfUJ8EG2hrdSw9fRj7waqNQChZ)}
\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\_scmpds\_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\_\_2 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_scpisort : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scmp\_gcd : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~k4\_numbers){\unicdcdcdhd}((k3\_finseq\_1~X3=X1){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~\\
X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~(k3\_finseq\_1~X3))){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_funct\_1~\\
X0~(k1\_scmp\_gcd~(k2\_nat\_1~X2~X4)))))))))\end{array}
\label{hyp:ehbdpfdhdgahjgdhpgcheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k4\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k5\_numbers){\unicdbdjdcd}((r1\_scpisort~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X3~(k3\_finseq\_1~\\
X0))){\unicdbdjdcd}(k1\_funct\_1~X0~X3=k1\_funct\_1~X1~(k1\_scmp\_gcd~(k2\_nat\_1~\\
X2~X3))))))))\end{array}
\label{hyp:egbdpfdhdgahjgdhpgcheh}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdhdgahjgdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~k4\_numbers){\unicdcdcdhd}((k3\_finseq\_1~X3=X1){\unicdcdcdhd}\\
(r1\_scpisort~X3~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
