\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{t40\_twoscomp (TMWAUnZxbzgX67HGhLw9okqodZJ2NYhmbAr)}
\maketitle
Let $ v1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k40\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_facirc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v3\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k34\_twoscomp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k15\_twoscomp : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}((v2\_circcomb~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~\\
X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~X1)))){\unicdbdjdcd}(((v1\_relat\_1~(k3\_msafree2~\\
X0)){\unicdcdcdhd}(v1\_relat\_1~(k3\_msafree2~X1))){\unicdbdjdcd}((v1\_facirc\_1~(k2\_msafree2~\\
X0)){\unicdcdcdid}((v1\_facirc\_1~(k2\_msafree2~X1)){\unicdcdcdid}(k2\_msafree2~(k2\_circcomb~\\
X0~X1)=k2\_xboole\_0~(k2\_msafree2~X0)~(k2\_msafree2~X1))))))\end{array}
\label{hyp:ehhdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_msafree2~(k5\_circcomb~X0~\\
(k10\_finseq\_1~X1~X2))=k2\_tarski~X1~X2\end{array}
\label{hyp:ehedadpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}(v1\_relat\_1~(k3\_msafree2~(k5\_circcomb~X0~X1)))\end{array}
\label{hyp:ehddidpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X0}}={X0}}}}\label{hyp:jgegfgngahpgehfgogdgfgpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k10\_finseq\_1~X0~X1))\end{array}
\label{hyp:ggdgidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xtuple\_0~X0){\unicdcdcdhd}(\preoh v1\_xtuple\_0~X1)){\unicdbdjdcd}\\
(\preoh v1\_facirc\_1~(k2\_tarski~X0~X1))\end{array}
\label{hyp:ggdgcdpfggbgdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_finseq\_1}~{({{{k10\_finseq\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdgbdadpfggjgogdhfgbhpfbd}
\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:ehedadpfehhhpgdhdgpgngah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xtuple\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xtuple\_0~X1){\unicdbdjdcd}\\
(k2\_msafree2~(k40\_twoscomp~X0~X1)=k2\_tarski~X0~X1))\end{array}$$
\end{theorem}
\end{document}
