\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t15\_scmfsa8a (TMbSdD9gMUbjqHiYCU6FckiQAGPfyZYtnEG)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa8a : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k11\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\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\_scmfsa\_2 : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k9\_xtuple\_0~\\
(k16\_funcop\_1~k6\_numbers~(k11\_scmfsa\_2~X0))=k1\_tarski~k6\_numbers){\unicdcdcdhd}\\
((k6\_numbers \in k9\_xtuple\_0~(k16\_funcop\_1~k6\_numbers~(k11\_scmfsa\_2~\\
X0))){\unicdcdcdhd}((k1\_funct\_1~(k16\_funcop\_1~k6\_numbers~(k11\_scmfsa\_2~X0))~\\
k6\_numbers=k11\_scmfsa\_2~X0){\unicdcdcdhd}((k5\_card\_1~(k16\_funcop\_1~k6\_numbers~\\
(k11\_scmfsa\_2~X0))=np\_\_1){\unicdcdcdhd}(\preoh k2\_compos\_1~k1\_scmfsa\_2 \in k10\_xtuple\_0~\\
(k16\_funcop\_1~k6\_numbers~(k11\_scmfsa\_2~X0)))))))\end{array}
\label{hyp:mgbdedpfdhdgngggdhbgidbg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_scmfsa8a~\\
X0=k16\_funcop\_1~k6\_numbers~(k11\_scmfsa\_2~X0))\end{array}
\label{hyp:egbdpfdhdgngggdhbgidbg}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfdhdgngggdhbgidbg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k5\_card\_1~\\
(k1\_scmfsa8a~X0)=np\_\_1)\end{array}$$
\end{theorem}
\end{document}
