\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t43\_twoscomp (TMMEtpPAXcQDoZZaXjte7E71e8kWU9TET7K)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k34\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k35\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_circuit2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k36\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_twoscomp : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~\\
k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k4\_card\_3~(u3\_msualg\_1~\\
(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~(k6\_facirc\_1~X0~X1~X2)))){\unicdbdjdcd}\\
((k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~\\
(k6\_facirc\_1~X0~X1~X2)~X3)~(k4\_tarski~(k10\_finseq\_1~X0~X1)~X2)=k1\_funct\_1~\\
X2~(k10\_finseq\_1~(k1\_funct\_1~X3~X0)~(k1\_funct\_1~X3~X1))){\unicdcdcdhd}((k1\_funct\_1~\\
(k6\_circuit2~(k5\_circcomb~X2~(k10\_finseq\_1~X0~X1))~(k6\_facirc\_1~\\
X0~X1~X2)~X3)~X0=k1\_funct\_1~X3~X0){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~(k5\_circcomb~\\
X2~(k10\_finseq\_1~X0~X1))~(k6\_facirc\_1~X0~X1~X2)~X3)~X1=k1\_funct\_1~\\
X3~X1))))\end{array}
\label{hyp:ehfdadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k15\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k15\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k15\_twoscomp~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgbdfdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k36\_twoscomp~X0~X1=k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~k15\_twoscomp\end{array}
\label{hyp:egddfdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k35\_twoscomp~X0~X1=k6\_facirc\_1~X0~X1~k15\_twoscomp\end{array}
\label{hyp:egddedpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k34\_twoscomp~X0~X1=k5\_circcomb~k15\_twoscomp~\\
(k10\_finseq\_1~X0~X1)\end{array}
\label{hyp:egddddpfehhhpgdhdgpgngah}
\end{equation}
\begin{theorem}\label{thm:ehedddpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k4\_card\_3~(u3\_msualg\_1~(k34\_twoscomp~\\
X0~X1)~(k35\_twoscomp~X0~X1)))){\unicdbdjdcd}((k1\_funct\_1~(k6\_circuit2~(k34\_twoscomp~\\
X0~X1)~(k35\_twoscomp~X0~X1)~X2)~(k36\_twoscomp~X0~X1)=k1\_funct\_1~\\
k15\_twoscomp~(k10\_finseq\_1~(k1\_funct\_1~X2~X0)~(k1\_funct\_1~X2~X1))){\unicdcdcdhd}\\
((k1\_funct\_1~(k6\_circuit2~(k34\_twoscomp~X0~X1)~(k35\_twoscomp~\\
X0~X1)~X2)~X0=k1\_funct\_1~X2~X0){\unicdcdcdhd}(k1\_funct\_1~(k6\_circuit2~(k34\_twoscomp~\\
X0~X1)~(k35\_twoscomp~X0~X1)~X2)~X1=k1\_funct\_1~X2~X1)))))\end{array}$$
\end{theorem}
\end{document}
