\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{t36\_twoscomp (TMGyLUQyQNd7a9hy7DmNzr1HipP6GHEmtmj)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k40\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_twoscomp : {\iota}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k37\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k34\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in u1\_struct\_0~(k5\_circcomb~\\
X2~(k10\_finseq\_1~X0~X1))){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k5\_circcomb~X2~(k10\_finseq\_1~\\
X0~X1))){\unicdcdcdhd}(k4\_tarski~(k10\_finseq\_1~X0~X1)~X2 \in u1\_struct\_0~(k5\_circcomb~\\
X2~(k10\_finseq\_1~X0~X1))))\end{array}
\label{hyp:ehedddpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X2 \in u1\_struct\_0~(k2\_circcomb~X0~X1)){\unicdcdcdhd}(\\
X2 \in u1\_struct\_0~(k2\_circcomb~X1~X0)))))\end{array}
\label{hyp:ehcdadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v2\_struct\_0~(k37\_twoscomp~X0~X1)){\unicdcdcdhd}((\\
\preoh v11\_struct\_0~(k37\_twoscomp~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k37\_twoscomp~\\
X0~X1)){\unicdcdcdhd}((v1\_circcomb~(k37\_twoscomp~X0~X1)){\unicdcdcdhd}((v2\_circcomb~(k37\_twoscomp~\\
X0~X1)){\unicdcdcdhd}((v3\_circcomb~(k37\_twoscomp~X0~X1)){\unicdcdcdhd}(l1\_msualg\_1~(k37\_twoscomp~\\
X0~X1)))))))\end{array}
\label{hyp:egehpflgddhdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v2\_struct\_0~(k34\_twoscomp~X0~X1)){\unicdcdcdhd}((\\
\preoh v11\_struct\_0~(k34\_twoscomp~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k34\_twoscomp~\\
X0~X1)){\unicdcdcdhd}((v1\_circcomb~(k34\_twoscomp~X0~X1)){\unicdcdcdhd}((v2\_circcomb~(k34\_twoscomp~\\
X0~X1)){\unicdcdcdhd}((v3\_circcomb~(k34\_twoscomp~X0~X1)){\unicdcdcdhd}(l1\_msualg\_1~(k34\_twoscomp~\\
X0~X1)))))))\end{array}
\label{hyp:egehpflgddedpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k40\_twoscomp~X0~X1=k2\_circcomb~(k34\_twoscomp~\\
X0~X1)~(k37\_twoscomp~X0~X1)\end{array}
\label{hyp:egddjdpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k37\_twoscomp~X0~X1=k5\_circcomb~k3\_twoscomp~\\
(k10\_finseq\_1~X0~X1)\end{array}
\label{hyp:egddgdpfehhhpgdhdgpgngah}
\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:ehddgdpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
((X0 \in u1\_struct\_0~(k40\_twoscomp~X0~X1)){\unicdcdcdhd}((X1 \in u1\_struct\_0~(k40\_twoscomp~\\
X0~X1)){\unicdcdcdhd}((k4\_tarski~(k10\_finseq\_1~X0~X1)~k15\_twoscomp \in u1\_struct\_0~\\
(k40\_twoscomp~X0~X1)){\unicdcdcdhd}(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp \in \\
u1\_struct\_0~(k40\_twoscomp~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
