\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{t4\_scmfsa9a (TMa8uLEr1GYDbQqiGA9WQPoPxvkFjfmscFH)}
\maketitle
Let $ k4\_sf\_mastr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_sf\_mastr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}((\preoh (X3{\unicdcdgdad}k2\_compos\_1~\\
k1\_scmfsa\_2){\unicdcdcdhd}((X3{\unicdcdgdad}k6\_scmfsa\_2~X0~X1){\unicdcdcdhd}((X3{\unicdcdgdad}k7\_scmfsa\_2~X0~X1){\unicdcdcdhd}\\
((X3{\unicdcdgdad}k8\_scmfsa\_2~X0~X1){\unicdcdcdhd}((X3{\unicdcdgdad}k9\_scmfsa\_2~X0~X1){\unicdcdcdhd}((X3{\unicdcdgdad}k10\_scmfsa\_2~\\
X0~X1){\unicdcdcdhd}((X3{\unicdcdgdad}k11\_scmfsa\_2~X2){\unicdcdcdhd}((X3{\unicdcdgdad}k12\_scmfsa\_2~X2~X0){\unicdcdcdhd}(X3{\unicdcdgdad}k13\_scmfsa\_2~\\
X2~X0))))))))){\unicdbdjdcd}(k3\_sf\_mastr~X3=k1\_xboole\_0)))))\end{array}
\label{hyp:ehddcdpfdhggpfngbgdhehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdbdjdcd}(k4\_sf\_mastr~(k16\_funcop\_1~\\
X0~X1)=k3\_sf\_mastr~X1))\end{array}
\label{hyp:ehcdpfdhdgngggdhbgjdbg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{{m1\_subset\_1}~{X0}}~{({{u1\_struct\_0}~{k1\_scmfsa\_2}})}})}{\unicdcdcdhd}{({{v1\_ami\_2}~{X0}})}}}\label{hyp:chdgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{m2\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}~{k5\_numbers}}\label{hyp:egehpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_compos\_1~X0)~(u1\_compos\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:egehpflgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_afinsq\_1}~{X0}}={{{k16\_funcop\_1}~{k6\_numbers}}~{X0}}}}\label{hyp:egbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_compos\_1~X0){\unicdbdjdcd}(k4\_compos\_1~X0=k3\_afinsq\_1~(k2\_compos\_1~\\
X0))\end{array}
\label{hyp:egbdgdpfdgpgngahpgdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfdhdgngggdhbgjdbg}
${{{k4\_sf\_mastr}~{({{k4\_compos\_1}~{k1\_scmfsa\_2}})}}={k1\_xboole\_0}}$.
\end{theorem}
\end{document}
