\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t26\_int\_6 (TMQQa88m3xaX7gGepEYZjVEGL7mGoCtkwJ4)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_int\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v1\_partfun3~X0){\unicdcdcdhd}\\
(v1\_int\_6~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_int\_6~X1~X0){\unicdbdjdcd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))\end{array}
\label{hyp:egehpfngbdpfjgogehpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v1\_partfun3~X0){\unicdcdcdhd}\\
(v1\_int\_6~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}((m1\_int\_6~X1~X0){\unicdbdjded}((k3\_finseq\_1~X1=k3\_finseq\_1~\\
X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(\preoh (X2 \in k4\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(v1\_int\_1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_int\_1~X4){\unicdbdjdcd}(\preoh (X4=k7\_xcmplx\_0~(\\
k19\_rvsum\_1~X0)~(k1\_funct\_1~X0~X2)){\unicdcdcdhd}((r2\_int\_1~(k3\_xcmplx\_0~X3~\\
X4)~np\_\_1~(k1\_funct\_1~X0~X2)){\unicdcdcdhd}(k1\_funct\_1~X1~X2=k3\_xcmplx\_0~X3~\\
(k7\_xcmplx\_0~(k19\_rvsum\_1~X0)~(k1\_funct\_1~X0~X2))))))))))))\end{array}
\label{hyp:egedpfjgogehpfgd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfjgogehpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}((v1\_partfun3~X0){\unicdcdcdhd}\\
(v1\_int\_6~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_int\_6~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((X2 \in k4\_finseq\_1~X1){\unicdbdjdcd}(r2\_int\_1~(k1\_funct\_1~\\
X1~X2)~np\_\_1~(k1\_funct\_1~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
