\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{t18\_calcul\_1 (TML6GC1qygyvhSx65fJvukRuYQGTSt27JuZ)}
\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 $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_calcul\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_cqc\_lang : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_calcul\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r10\_calcul\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ m1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r9\_calcul\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}(\preoh (\preoh r1\_xxreal\_0~(k3\_finseq\_1~X1)~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~(\\
k3\_finseq\_1~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~X1))~k6\_numbers)))\end{array}
\label{hyp:ehedpfdgbgmgdgfhmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_funct\_2~X2~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_valuat\_1~X4~X0~X1){\unicdbdjdcd}((r1\_valuat\_1~X0~X1~(k6\_cqc\_lang~\\
X0~X3)~X4~X2){\unicdbdjded}(\preoh r1\_valuat\_1~X0~X1~X3~X4~X2))))))\end{array}
\label{hyp:ehbdhdpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m1\_valuat\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~(\\
k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~\\
X4~(k3\_cqc\_lang~X0)){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X4)~k6\_numbers){\unicdbdjdcd}\\
(((r9\_calcul\_1~X0~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~X4)~X1~X2~X3){\unicdcdcdhd}(\\
r1\_valuat\_1~X0~X1~(k2\_calcul\_1~X0~X4)~X2~X3)){\unicdbdjded}(r9\_calcul\_1~X0~X4~\\
X1~X2~X3)))))))\end{array}
\label{hyp:ehbdhdpfdgbgmgdgfhmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
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}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_cqc\_lang}~{X0}})}}}})}}}\label{hyp:ggdgcdpfdgbhdgpfmgbgoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\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}(m2\_subset\_1~(k2\_calcul\_1~X0~X1)~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0))\end{array}
\label{hyp:egehpflgcdpfdgbgmgdgfhmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_1~(k1\_calcul\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdpfdgbgmgdgfhmgpfbd}
\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 .  (m2\_subset\_1~X2~(k9\_qc\_lang1~X0)~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}((r10\_calcul\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (\preoh v1\_xboole\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_valuat\_1~X4~X0~X3){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_funct\_2~X5~\\
(k3\_qc\_lang1~X0)~X3~(k2\_valuat\_1~X0~X3)){\unicdbdjdcd}((r9\_calcul\_1~X0~X1~X3~\\
X4~X5){\unicdbdjdcd}(r1\_valuat\_1~X0~X3~X2~X4~X5))))))))\end{array}
\label{hyp:egbdfdpfdgbgmgdgfhmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdgbgmgdgfhmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_cqc\_lang~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(k3\_cqc\_lang~X0)){\unicdbdjdcd}(((r2\_relset\_1~\\
k5\_numbers~(k3\_cqc\_lang~X0)~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~(k1\_calcul\_1~\\
(k3\_cqc\_lang~X0)~X1))~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~(k1\_calcul\_1~\\
(k3\_cqc\_lang~X0)~X2))){\unicdcdcdhd}((k6\_cqc\_lang~X0~(k2\_calcul\_1~X0~(k1\_calcul\_1~\\
(k3\_cqc\_lang~X0)~X1))=k2\_calcul\_1~X0~(k1\_calcul\_1~(k3\_cqc\_lang~\\
X0)~X2)){\unicdcdcdhd}((k2\_calcul\_1~X0~X1=k2\_calcul\_1~X0~X2){\unicdcdcdhd}((r10\_calcul\_1~\\
X0~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~X1)~(k2\_calcul\_1~X0~X1)){\unicdcdcdhd}(r10\_calcul\_1~\\
X0~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~X2)~(k2\_calcul\_1~X0~X2)))))){\unicdbdjdcd}\\
((r1\_xxreal\_0~(k3\_finseq\_1~X1)~np\_\_1){\unicdcdcdid}((r1\_xxreal\_0~(k3\_finseq\_1~\\
X2)~np\_\_1){\unicdcdcdid}(r10\_calcul\_1~X0~(k1\_calcul\_1~(k3\_cqc\_lang~X0)~(k1\_calcul\_1~\\
(k3\_cqc\_lang~X0)~X1))~(k2\_calcul\_1~X0~X1)))))))\end{array}$$
\end{theorem}
\end{document}
