\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{t108\_gfacirc1 (TMGLVZFTXYkHsHWKkkYkZRia4nR551VquKy)}
\maketitle
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_twoscomp : {\iota}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k41\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\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 $ r1\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_circcomb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_circcomb : {{\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 $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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 $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k3\_enumset1~\\
X0~X1~X2~X3~X4=k2\_xboole\_0~(k1\_enumset1~X0~X1~X2)~(k2\_tarski~X3~X4)\end{array}
\label{hyp:ehjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_enumset1~X2~X3~X0~X1\end{array}
\label{hyp:ehhdddpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_enumset1~X1~X3~X2~X0\end{array}
\label{hyp:ehhdadpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_xboole\_0~(k1\_enumset1~X0~X1~X2)~(k1\_tarski~X3)\end{array}
\label{hyp:ehgdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_enumset1~X1~X2~X0~X3\end{array}
\label{hyp:ehgdhdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k4\_xboole\_0~(k2\_tarski~X0~X1)~\\
X2=k2\_tarski~X0~X1){\unicdbdjded}((\preoh X0 \in X2){\unicdcdcdhd}(\preoh X1 \in X2))\end{array}
\label{hyp:ehgdddpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_xboole\_0~(k2\_tarski~X0~X1)~(k2\_tarski~X2~X3)\end{array}
\label{hyp:ehfdpffgogfhngdhfgehbd}
\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}((r1\_circcomb~X0~X1){\unicdbdjdcd}(\\
k2\_msafree2~(k2\_circcomb~X0~X1)=k2\_xboole\_0~(k4\_xboole\_0~(k2\_msafree2~\\
X0)~(k3\_msafree2~X1))~(k4\_xboole\_0~(k2\_msafree2~X1)~(k3\_msafree2~\\
X0)))))\end{array}
\label{hyp:ehfdpfdgjgchdgdgngcgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k1\_enumset1~X0~X1~X2=k1\_enumset1~\\
X1~X0~X2\end{array}
\label{hyp:ehfdidpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{{k4\_xboole\_0}~{X0}}~{({{k1\_tarski}~{X1}})}}={X0}})}{\unicdbdjded}{({\preoh{{{X1} \in {X0}}}})}}}}\label{hyp:ehfdhdpfkhggngjgdhdgpfbd}
\end{equation}
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}(r1\_circcomb~X0~X1))\end{array}
\label{hyp:ehedhdpfdgjgchdgdgpgngcg}
\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}((k2\_msafree2~(k5\_circcomb~X0~X1)=k10\_xtuple\_0~X1){\unicdcdcdhd}(k3\_msafree2~\\
(k5\_circcomb~X0~X1)=k1\_tarski~(k4\_tarski~X1~X0)))\end{array}
\label{hyp:ehedcdpfdgjgchdgdgpgngcg}
\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 .  {\unicdcdadad} X2 .  k2\_enumset1~X0~X0~X1~X2=k1\_enumset1~\\
X0~X1~X2\end{array}
\label{hyp:ehddbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X0~X1)~X2){\unicdcdcdhd}(X1{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X0~X1)~X2)\end{array}
\label{hyp:ehcdpfggbgdgjgchdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(k6\_subset\_1~\\
(k2\_tarski~X0~X1)~(k1\_tarski~X2){\unicdcdgdad}k2\_tarski~X0~X1))\end{array}
\label{hyp:ehbdpfggbgdgjgchdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_tarski~X0~X1=k2\_xboole\_0~(k1\_tarski~\\
X0)~(k1\_tarski~X1)\end{array}
\label{hyp:ehbdpffgogfhngdhfgehbd}
\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}((r1\_circcomb~X0~X1){\unicdbdjdcd}(\\
(k3\_msafree2~(k2\_circcomb~X0~X1)=k2\_xboole\_0~(k3\_msafree2~X0)~\\
(k3\_msafree2~X1)){\unicdcdcdhd}(r1\_tarski~(k2\_msafree2~(k2\_circcomb~X0~X1))~\\
(k2\_xboole\_0~(k2\_msafree2~X0)~(k2\_msafree2~X1))))))\end{array}
\label{hyp:ehbdbdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k3\_enumset1~\\
X0~X1~X2~X3~X4=k2\_xboole\_0~(k2\_enumset1~X0~X1~X2~X3)~(k1\_tarski~X4)\end{array}
\label{hyp:ehbdadpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~(k4\_finseq\_2~np\_\_2~\\
k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~\\
k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1))))){\unicdbdjdcd}({\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 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
\preoh (X3{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X4~X5)~X1){\unicdcdcdhd}((X4{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X5~X3)~X2){\unicdcdcdhd}((X5{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X3~X4)~X0){\unicdcdcdhd}(\preoh (\preoh k4\_tarski~\\
(k10\_finseq\_1~X3~X4)~X0 \in k2\_tarski~X4~X5){\unicdcdcdhd}((\preoh X5 \in k2\_tarski~(k4\_tarski~\\
(k10\_finseq\_1~X3~X4)~X0)~(k4\_tarski~(k10\_finseq\_1~X4~X5)~X1)){\unicdcdcdhd}(\\
(\preoh X3 \in k2\_tarski~(k4\_tarski~(k10\_finseq\_1~X3~X4)~X0)~(k4\_tarski~\\
(k10\_finseq\_1~X4~X5)~X1)){\unicdcdcdhd}(\preoh k4\_tarski~(k10\_finseq\_1~X5~X3)~X2 \in \\
k1\_enumset1~X3~X4~X5)))))))))\end{array}
\label{hyp:mgbdedpfhgggbgdgjgchdgbd}
\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}((\preoh v2\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((\preoh v11\_struct\_0~(\\
k5\_circcomb~X0~X1)){\unicdcdcdhd}(v1\_msualg\_1~(k5\_circcomb~X0~X1))))\end{array}
\label{hyp:ggdgjdpfdgjgchdgdgpgngcg}
\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 v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}(\\
(\preoh v2\_struct\_0~(k2\_circcomb~X1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k2\_circcomb~\\
X1~X0)){\unicdcdcdhd}(v1\_msualg\_1~(k2\_circcomb~X1~X0))))\end{array}
\label{hyp:ggdghdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_circcomb~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k2\_circcomb~\\
X0~X1)){\unicdcdcdhd}(v2\_circcomb~(k2\_circcomb~X0~X1))))\end{array}
\label{hyp:ggdgbdcdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_circcomb~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v1\_circcomb~X1){\unicdcdcdhd}(l1\_msualg\_1~\\
X1)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k2\_circcomb~\\
X0~X1)){\unicdcdcdhd}(v1\_circcomb~(k2\_circcomb~X0~X1))))\end{array}
\label{hyp:ggdgbdbdpfdgjgchdgdgpgngcg}
\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 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((\preoh v11\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k5\_circcomb~\\
X0~X1)){\unicdcdcdhd}((v1\_circcomb~(k5\_circcomb~X0~X1)){\unicdcdcdhd}(v2\_circcomb~(k5\_circcomb~\\
X0~X1)))))\end{array}
\label{hyp:ggdgbdadpfdgjgchdgdgpgngcg}
\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}((\preoh v11\_struct\_0~(k5\_circcomb~X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k5\_circcomb~\\
X0~X1)){\unicdcdcdhd}(l1\_msualg\_1~(k5\_circcomb~X0~X1))))\end{array}
\label{hyp:egehpflgfdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_twoscomp){\unicdcdcdhd}((v1\_funct\_2~k4\_twoscomp~(k4\_finseq\_2~\\
np\_\_2~k6\_margrel1)~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~k4\_twoscomp~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k4\_finseq\_2~np\_\_2~k6\_margrel1)~k6\_margrel1))))\end{array}
\label{hyp:egehpflgedpfehhhpgdhdgpgngah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k2\_circcomb~\\
X0~X1)){\unicdcdcdhd}((v1\_msualg\_1~(k2\_circcomb~X0~X1)){\unicdcdcdhd}(l1\_msualg\_1~(k2\_circcomb~\\
X0~X1))))\end{array}
\label{hyp:egehpflgcdpfdgjgchdgdgpgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k41\_gfacirc1~X0~X1~X2=k2\_circcomb~\\
(k2\_circcomb~(k5\_circcomb~k4\_twoscomp~(k10\_finseq\_1~X0~X1))~(\\
k5\_circcomb~k4\_twoscomp~(k10\_finseq\_1~X1~X2)))~(k5\_circcomb~k4\_twoscomp~\\
(k10\_finseq\_1~X2~X0))\end{array}
\label{hyp:egedbdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}(k3\_msafree2~\\
X0=k2\_relset\_1~(u1\_struct\_0~X0)~(u2\_msualg\_1~X0))\end{array}
\label{hyp:egddpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}(k2\_msafree2~\\
X0=k6\_subset\_1~(u1\_struct\_0~X0)~(k2\_relset\_1~(u1\_struct\_0~X0)~\\
(u2\_msualg\_1~X0)))\end{array}
\label{hyp:egcdpfngdhbgggchfgfgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_msualg\_1~X0){\unicdbdjdcd}((v1\_msualg\_1~X0){\unicdbdjdcd}(X0=g1\_msualg\_1~\\
(u1\_struct\_0~X0)~(u4\_struct\_0~X0)~(u1\_msualg\_1~X0)~(u2\_msualg\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfngdhfhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadidpfhgggbgdgjgchdgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X0{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k4\_twoscomp){\unicdcdcdhd}((X1{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X2~X0)~k4\_twoscomp){\unicdcdcdhd}\\
((X2{\unicdcdgdad}k4\_tarski~(k10\_finseq\_1~X0~X1)~k4\_twoscomp){\unicdcdcdhd}(k2\_msafree2~\\
(k41\_gfacirc1~X0~X1~X2){\unicdcdgdad}k1\_enumset1~X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
