\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{t7\_scmfsa8a (TMMdwixGVdhThDZXEg34JKnfA1QxbsaC41x)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa6a : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(k1\_funct\_1~X1~X0=X2)){\unicdbdjdcd}(k1\_funct\_1~\\
(k6\_funct\_4~X1~X2~X3)~X0=X3))\end{array}
\label{hyp:ehbdadgdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (k1\_funct\_1~X1~X0{\unicdcdgdad}X2){\unicdbdjdcd}(k1\_funct\_1~(k6\_funct\_4~X1~X2~\\
X3)~X0=k1\_funct\_1~X1~X0))\end{array}
\label{hyp:ehbdadfdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~\\
X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(k1\_scmfsa6a~X0~X1=k6\_funct\_4~X0~(k2\_compos\_1~k1\_scmfsa\_2)~(k11\_scmfsa\_2~\\
X1)))\end{array}
\label{hyp:egbdpfdhdgngggdhbggdbg}
\end{equation}
\begin{theorem}\label{thm:ehhdpfdhdgngggdhbgidbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~\\
X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(((k1\_funct\_1~X0~X2=k2\_compos\_1~\\
k1\_scmfsa\_2){\unicdbdjdcd}(k1\_funct\_1~(k1\_scmfsa6a~X0~X1)~X2=k11\_scmfsa\_2~\\
X1)){\unicdcdcdhd}((k1\_funct\_1~X0~X2{\unicdcdgdad}k2\_compos\_1~k1\_scmfsa\_2){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_scmfsa6a~X0~X1)~X2=k1\_funct\_1~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
