\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t10\_midsp\_3 (TMKXJz4Q3f8gZbjv376ywSv1efwnCEdjVpx)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m1\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_midsp\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}((m1\_midsp\_3~X0~X1){\unicdbdjded}(X0 \in k2\_finseq\_1~(k2\_nat\_1~\\
X1~np\_\_1))))\end{array}
\label{hyp:ehhdpfngjgegdhahpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_midsp\_1~\\
X2){\unicdcdcdhd}(l1\_midsp\_3~X2~(k2\_nat\_1~X1~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~(u1\_struct\_0~\\
X2)~(k4\_finseq\_2~(k2\_nat\_1~X1~np\_\_1)~(u1\_struct\_0~X2))){\unicdbdjdcd}((X0 \in \\
k2\_finseq\_1~(k2\_nat\_1~X1~np\_\_1)){\unicdbdjdcd}((k1\_funct\_1~(k1\_midsp\_3~(u1\_struct\_0~\\
X2)~(k2\_nat\_1~X1~np\_\_1)~X4~X0~X3)~X0=X3){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~k5\_numbers){\unicdbdjdcd}((X5 \in k7\_subset\_1~k5\_numbers~(k4\_finseq\_1~X4)~\\
(k1\_tarski~X0)){\unicdbdjdcd}(k1\_funct\_1~(k1\_midsp\_3~(u1\_struct\_0~X2)~(k2\_nat\_1~\\
X1~np\_\_1)~X4~X0~X3)~X5=k1\_funct\_1~X4~X5)))))))))\end{array}
\label{hyp:ehgdpfngjgegdhahpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfngjgegdhahpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_midsp\_1~\\
X2){\unicdcdcdhd}(l1\_midsp\_3~X2~(k2\_nat\_1~X0~np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~X4~(u1\_struct\_0~\\
X2)~(k4\_finseq\_2~(k2\_nat\_1~X0~np\_\_1)~(u1\_struct\_0~X2))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_midsp\_3~X5~X0){\unicdbdjdcd}((X5=X1){\unicdbdjdcd}(k1\_funct\_1~(k1\_midsp\_3~(u1\_struct\_0~\\
X2)~(k2\_nat\_1~X0~np\_\_1)~X4~X1~X3)~X5=X3)))))))\end{array}$$
\end{theorem}
\end{document}
