\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{t66\_pnproc\_1 (TMRnNYV1sDDvzP5DGqAHhoNopW8psQ1jNYJ)}
\maketitle
Let $ m2\_pnproc\_1 : {{\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 $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k11\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}(k11\_pnproc\_1~X0~X1~X2~X3=ReplSep~\\
(toset~({\uniddcgcg} X4 : \iota .  m2\_finseq\_2~X4~X1~(k3\_finseq\_2~X1)))~({\uniddcgcg} X4 : \\
\iota .  {\unicdcdaddd} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}(v2\_finseq\_1~\\
X5))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v2\_finseq\_1~\\
X6))){\unicdcdcdhd}((X4=k2\_xboole\_0~X5~X6){\unicdcdcdhd}((r1\_xboole\_0~X5~X6){\unicdcdcdhd}((k15\_finseq\_1~\\
X5 \in X2){\unicdcdcdhd}(k15\_finseq\_1~X6 \in X3))))))~({\uniddcgcg} X4 : \iota .  X4))))\end{array}
\label{hyp:egbdddpfahogahchpgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdgdpfahogahchpgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_pnproc\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k3\_finseq\_2~X1))){\unicdbdjdcd}(((r1\_tarski~X2~X3){\unicdcdcdhd}(r1\_tarski~\\
X4~X5)){\unicdbdjdcd}(r1\_tarski~(k11\_pnproc\_1~X0~X1~X2~X4)~(k11\_pnproc\_1~X0~X1~\\
X3~X5)))))))\end{array}$$
\end{theorem}
\end{document}
