\documentclass{article}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t18\_borsuk\_7 (TMV6B4TmWHeLkHoRz1wZjgd6prXhmmuzH99)}
\maketitle
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k39\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~X2))){\unicdbdjdcd}(k24\_valued\_1~\\
(k24\_valued\_1~X2~X0)~X1=k24\_valued\_1~X2~(k3\_xcmplx\_0~X0~X1))))\end{array}
\label{hyp:ehbdgdpfghbgmgfhfgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}(k24\_valued\_1~(k18\_valued\_1~\\
X0~X1)~X2=k18\_valued\_1~(k24\_valued\_1~X0~X2)~X1)))\end{array}
\label{hyp:ehbdcdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k39\_valued\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k39\_valued\_1~\\
X0)){\unicdcdcdhd}(v1\_valued\_0~(k39\_valued\_1~X0))))\end{array}
\label{hyp:ggdghdadpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}((v1\_relat\_1~(k24\_valued\_1~X0~X1)){\unicdcdcdhd}\\
((v1\_funct\_1~(k24\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_valued\_0~(k24\_valued\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgededpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
(k39\_valued\_1~X0=k18\_valued\_1~X0~X0)\end{array}
\label{hyp:egidpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_square\_1}~{X0}}={{{k3\_xcmplx\_0}~{X0}}~{X0}}})}}}\label{hyp:egbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1)))){\unicdbdjdcd}\\
(k18\_valued\_1~X0~X1=k18\_valued\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdidpfghbgmgfhfgegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfcgpgchdhfhlgpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1)))){\unicdbdjdcd}(k39\_valued\_1~\\
(k24\_valued\_1~X1~X0)=k24\_valued\_1~(k39\_valued\_1~X1)~(k3\_square\_1~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
