\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{t2\_valuat\_1 (TMRaq4HqvoSoweMDfc4XM7oJ72KPEAuevDn)}
\maketitle
Let $ m1\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_qc\_lang1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_valuat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ k12\_margrel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh k7\_margrel1 \in X0){\unicdbdjdcd}(k12\_margrel1~X0=k8\_margrel1)){\unicdcdcdhd}\\
((\preoh (k12\_margrel1~X0=k8\_margrel1){\unicdcdcdhd}(k7\_margrel1 \in X0)){\unicdcdcdhd}(((k7\_margrel1 \in \\
X0){\unicdbdjdcd}(k12\_margrel1~X0=k7\_margrel1)){\unicdcdcdhd}((k12\_margrel1~X0=k7\_margrel1){\unicdbdjdcd}\\
(k7\_margrel1 \in X0))))\end{array}
\label{hyp:ehbdhdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~X3~\\
X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgddpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{m1\_qc\_lang1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k2\_qc\_lang1}~{X0}})}}}})}}}\label{hyp:ggdgcdpfbhdgpfmgbgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k6\_margrel1}}}}\label{hyp:ggdgcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_qc\_lang1~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~(k3\_qc\_lang1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k9\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1))))){\unicdbdjdcd}(m2\_funct\_2~\\
(k3\_valuat\_1~X0~X1~X2~X3)~(k2\_valuat\_1~X0~X1)~k6\_margrel1~(k9\_funct\_2~\\
(k2\_valuat\_1~X0~X1)~k6\_margrel1))\end{array}
\label{hyp:egehpflgddpfghbgmgfhbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_qc\_lang1~X0)~(k1\_zfmisc\_1~\\
(k2\_qc\_lang1~X0)))\end{array}
\label{hyp:egehpflgddpfbhdgpfmgbgoghgbd}
\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\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_funct\_2~X3~(k2\_valuat\_1~X0~X1)~k6\_margrel1~(k9\_funct\_2~\\
(k2\_valuat\_1~X0~X1)~k6\_margrel1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~\\
(k2\_valuat\_1~X0~X1)~k6\_margrel1~(k9\_funct\_2~(k2\_valuat\_1~X0~X1)~\\
k6\_margrel1)){\unicdbdjdcd}((X4=k3\_valuat\_1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m2\_funct\_2~\\
X5~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)){\unicdbdjdcd}(k3\_funct\_2~(k2\_valuat\_1~\\
X0~X1)~k6\_margrel1~X4~X5=k12\_margrel1~(ReplSep~(toset~({\uniddcgcg} X6 : \\
\iota .  m2\_funct\_2~X6~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~X1)))~({\uniddcgcg} X6 : \\
\iota .  {\unicdcdadad} X7 .  (m2\_subset\_1~X7~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~\\
X0)){\unicdbdjdcd}((X2{\unicdcdgdad}X7){\unicdbdjdcd}(k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X6~X7=k3\_funct\_2~\\
(k3\_qc\_lang1~X0)~X1~X5~X7)))~({\uniddcgcg} X6 : \iota .  k3\_funct\_2~(k2\_valuat\_1~\\
X0~X1)~k6\_margrel1~X3~X6)))))))))\end{array}
\label{hyp:egcdpfghbgmgfhbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfghbgmgfhbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_qc\_lang1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_funct\_2~X3~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k2\_valuat\_1~X0~X1)~k6\_margrel1~\\
(k9\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1)){\unicdbdjdcd}((k3\_funct\_2~(\\
k2\_valuat\_1~X0~X1)~k6\_margrel1~(k3\_valuat\_1~X0~X1~X2~X4)~X3=k7\_margrel1){\unicdbdjded}\\
({\unicdcdaddd} X5 .  (m2\_funct\_2~X5~(k3\_qc\_lang1~X0)~X1~(k2\_valuat\_1~X0~\\
X1)){\unicdcdcdhd}((k3\_funct\_2~(k2\_valuat\_1~X0~X1)~k6\_margrel1~X4~X5=k7\_margrel1){\unicdcdcdhd}\\
({\unicdcdadad} X6 .  (m2\_subset\_1~X6~(k2\_qc\_lang1~X0)~(k3\_qc\_lang1~X0)){\unicdbdjdcd}\\
((X2{\unicdcdgdad}X6){\unicdbdjdcd}(k3\_funct\_2~(k3\_qc\_lang1~X0)~X1~X5~X6=k3\_funct\_2~(k3\_qc\_lang1~\\
X0)~X1~X3~X6))))))))))\end{array}$$
\end{theorem}
\end{document}
