\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{t46\_gfacirc1 (TMdMeqPGaGVkDgkT41z3hPmet1b3osGFWvW)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_facirc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k19\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k3\_gfacirc1 : {\iota}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k3\_twoscomp){\unicdcdcdhd}((X1{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X2~X0)~k2\_twoscomp){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_gfacirc1){\unicdcdcdhd}(k2\_msafree2~\\
(k19\_gfacirc1~X0~X1~X2){\unicdcdgdad}k1\_enumset1~X0~X1~X2)))\end{array}
\label{hyp:ehedfdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xtuple\_0~X0){\unicdcdcdhd}((\preoh v1\_xtuple\_0~\\
X1){\unicdcdcdhd}(\preoh v1\_xtuple\_0~X2))){\unicdbdjdcd}(\preoh v1\_facirc\_1~(k1\_enumset1~X0~X1~X2))\end{array}
\label{hyp:ggdgddpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xtuple\_0~X0){\unicdbdjded}({\unicdcdaddd} X1 .  {\unicdcdaddd} X2 .  X0=k4\_tarski~\\
X1~X2)\end{array}
\label{hyp:egbdpfihehfhahmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}(\preoh v1\_facirc\_1~(k2\_msafree2~(k19\_gfacirc1~\\
X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
