\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{t14\_substlat (TMQba85gtdvJJFDqXWYKbgC8dcGdiW1htK3)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X2 : \\
\iota{\unicdbdjdcd}\iota{\unicdbdjdcd}o .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~X4){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X3){\unicdbdjdcd}((X2~X5~X6){\unicdbdjdcd}(X1~X5~X6)))){\unicdbdjdcd}\\
(r1\_tarski~(ReplSep2~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~X4))~(\\
{\uniddcgcg} X5 : \iota .  toset~({\uniddcgcg} X6 : \iota .  m1\_subset\_1~X6~X3))~({\uniddcgcg} X5 : \iota .  \\
{\uniddcgcg} X6 : \iota .  X2~X5~X6)~({\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  X0~X5~X6))~(ReplSep2~\\
(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~X4))~({\uniddcgcg} X5 : \iota .  toset~({\uniddcgcg} X6 : \\
\iota .  m1\_subset\_1~X6~X3))~({\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  X1~X5~X6)~({\uniddcgcg} X5 : \\
\iota .  {\uniddcgcg} X6 : \iota .  X0~X5~X6)))\end{array}
\label{hyp:dhcdpfggchbgfgoglgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}(k4\_substlat~X0~X1~X2~X3=ReplSep2~(toset~\\
({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(k4\_partfun1~X0~X1)))~({\uniddcgcg} X4 : \iota .  \\
toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~(k4\_partfun1~X0~X1)))~({\uniddcgcg} X4 : \\
\iota .  {\uniddcgcg} X5 : \iota .  (X4 \in X2){\unicdcdcdhd}((X5 \in X3){\unicdcdcdhd}(r1\_partfun1~X4~X5)))~({\uniddcgcg} X4 : \\
\iota .  {\uniddcgcg} X5 : \iota .  k2\_xboole\_0~X4~X5)))\end{array}
\label{hyp:egddpfdhfhcgdhehmgbgeh}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfdhfhcgdhehmgbgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}((r1\_tarski~X2~X3){\unicdbdjdcd}(r1\_tarski~(k4\_substlat~\\
X0~X1~X2~X4)~(k4\_substlat~X0~X1~X3~X4)))))\end{array}$$
\end{theorem}
\end{document}
