\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{t75\_abcmiz\_1 (TMWDShY7mrnNvCo1hDCPkFYpCuRMeiCJriR)}
\maketitle
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_trees\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k28\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k34\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v9\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k36\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k13\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k31\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k33\_abcmiz\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_abcmiz\_1~X3~X0~(k12\_abcmiz\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_trees\_4~X4~(k3\_card\_3~(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~\\
X0))))~(k34\_abcmiz\_1~X0)){\unicdbdjdcd}(\preoh (k3\_finseq\_1~X4=k3\_finseq\_1~(k1\_msualg\_1~\\
X0~X1)){\unicdcdcdhd}(k36\_abcmiz\_1~X0~X1~X4=k31\_abcmiz\_1~X0~(k33\_abcmiz\_1~X0)~\\
X2~X3))))))\end{array}
\label{hyp:ehfdfdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_abcmiz\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_4~X2~(k3\_card\_3~(\\
u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~\\
X0)){\unicdbdjdcd}((k3\_finseq\_1~X2=k3\_finseq\_1~(k1\_msualg\_1~X0~X1)){\unicdbdjdcd}(m1\_abcmiz\_1~\\
(k36\_abcmiz\_1~X0~X1~X2)~X0~(k2\_msualg\_1~X0~X1)))))\end{array}
\label{hyp:ehfdcdpfbgcgdgngjgkhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_abcmiz\_1~X1~X0~(k12\_abcmiz\_1~\\
X0)){\unicdbdjdcd}((v9\_abcmiz\_1~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_abcmiz\_1~X2~X0~(k13\_abcmiz\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_abcmiz\_1~X3~X0~(k12\_abcmiz\_1~X0)){\unicdbdjdcd}(X1{\unicdcdgdad}k31\_abcmiz\_1~\\
X0~(k33\_abcmiz\_1~X0)~X2~X3)))))\end{array}
\label{hyp:egedbdpfbgcgdgngjgkhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdfdpfbgcgdgngjgkhpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_instalg1~X0){\unicdcdcdhd}((v1\_abcmiz\_1~X0){\unicdcdcdhd}((v3\_abcmiz\_1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_trees\_4~X1~(k3\_card\_3~\\
(u3\_msualg\_1~X0~(k1\_msafree3~X0~(k28\_abcmiz\_1~X0))))~(k34\_abcmiz\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v2\_abcmiz\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(u4\_struct\_0~\\
X0))){\unicdbdjdcd}(((k2\_msualg\_1~X0~X2=k12\_abcmiz\_1~X0){\unicdcdcdhd}(k3\_finseq\_1~X1=\\
k3\_finseq\_1~(k1\_msualg\_1~X0~X2))){\unicdbdjdcd}((v9\_abcmiz\_1~(k36\_abcmiz\_1~\\
X0~X2~X1)~X0){\unicdcdcdhd}(m1\_abcmiz\_1~(k36\_abcmiz\_1~X0~X2~X1)~X0~(k12\_abcmiz\_1~\\
X0))))))\end{array}$$
\end{theorem}
\end{document}
