\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}
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\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{t62\_calcul\_1 (TMZKWf4akpuA42AWyzLa4zP6kcefip5YFwi)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_cqc\_lang : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_calcul\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_cqc\_lang~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k3\_calcul\_1~X0~X1)~(k1\_zfmisc\_1~(k3\_qc\_lang1~\\
X0)))\end{array}
\label{hyp:egehpflgddpfdgbgmgdgfhmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k3\_qc\_lang1~X0))){\unicdbdjdcd}\\
((X2=k3\_calcul\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~k5\_numbers){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_subset\_1~X5~(k9\_qc\_lang1~X0)~(\\
k3\_cqc\_lang~X0)){\unicdcdcdhd}((X4 \in k1\_relset\_1~k5\_numbers~X1){\unicdcdcdhd}((X5=k1\_funct\_1~\\
X1~X4){\unicdcdcdhd}(X3 \in k24\_qc\_lang1~X0~X5)))))))))\end{array}
\label{hyp:egfdpfdgbgmgdgfhmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k3\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  (X2 \in X3){\unicdcdcdhd}(X3 \in X0)))\end{array}
\label{hyp:egedpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfdgbgmgdgfhmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}(k3\_calcul\_1~X0~X1=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  \\
m2\_subset\_1~X2~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)))~({\uniddcgcg} X2 : \iota .  \\
{\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_numbers){\unicdcdcdhd}((X3 \in k1\_relset\_1~k5\_numbers~\\
X1){\unicdcdcdhd}(X2=k1\_funct\_1~X1~X3)))~({\uniddcgcg} X2 : \iota .  k24\_qc\_lang1~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
