\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{t16\_ftacell1 (TMMBVzgjmkS9BiVCR7bFX9iDnS1oEXzXmgR)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_twoscomp : {\iota}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k25\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_ftacell1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k3\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\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}({\unicdcdadad} X3 .  (\preoh v1\_xtuple\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~(k24\_gfacirc1~X0~\\
X1~X2))~k4\_twoscomp){\unicdcdcdhd}((\preoh X4 \in k3\_msafree2~(k25\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
(k2\_msafree2~(k7\_ftacell1~X0~X1~X2~X3~X4){\unicdcdgdad}k3\_enumset1~X0~X1~X2~X3~\\
X4))))))\end{array}
\label{hyp:ehbdddpfggehbgdgfgmgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(X5=k3\_enumset1~X0~X1~X2~X3~X4){\unicdbdjded}({\unicdcdadad} X6 .  (X6 \in X5){\unicdbdjded}(\preoh (X6{\unicdcdgdad}X0){\unicdcdcdhd}\\
((X6{\unicdcdgdad}X1){\unicdcdcdhd}((X6{\unicdcdgdad}X2){\unicdcdcdhd}((X6{\unicdcdgdad}X3){\unicdcdcdhd}(X6{\unicdcdgdad}X4))))))\end{array}
\label{hyp:egddpffgogfhngdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfggehbgdgfgmgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (\preoh v1\_xtuple\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\preoh v1\_xtuple\_0~X3){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  \preoh (X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~(k24\_gfacirc1~X0~\\
X1~X2))~k4\_twoscomp){\unicdcdcdhd}((\preoh X4 \in k3\_msafree2~(k25\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
(\preoh (X0 \in k2\_msafree2~(k7\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((X1 \in k2\_msafree2~\\
(k7\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}((X2 \in k2\_msafree2~(k7\_ftacell1~X0~\\
X1~X2~X3~X4)){\unicdcdcdhd}((X3 \in k2\_msafree2~(k7\_ftacell1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(X4 \in \\
k2\_msafree2~(k7\_ftacell1~X0~X1~X2~X3~X4)))))))))))\end{array}$$
\end{theorem}
\end{document}
