\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t7\_facirc\_2 (TMR3nVSdKy1Lv9tt5bbNnoKACF9cLfciiSf)}
\maketitle
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 $ k3\_facirc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_margrel1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_facirc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_facirc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_msafree2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k17\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k20\_facirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))))){\unicdbdjdcd}(m2\_subset\_1~(k5\_facirc\_2~\\
X0~X1~X2)~(u1\_struct\_0~(k3\_facirc\_2~X0~X1~X2))~(k3\_msafree2~(k3\_facirc\_2~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpflgfdpfggbgdgjgchdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))))){\unicdbdjdcd}((v3\_msualg\_1~(k4\_facirc\_2~\\
X0~X1~X2)~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_msafree2~(k4\_facirc\_2~X0~\\
X1~X2)~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_circcomb~(k4\_facirc\_2~X0~X1~\\
X2)~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}((v6\_circcomb~(k4\_facirc\_2~X0~X1~X2)~\\
(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}(l3\_msualg\_1~(k4\_facirc\_2~X0~X1~X2)~(k3\_facirc\_2~\\
X0~X1~X2))))))\end{array}
\label{hyp:egehpflgedpfggbgdgjgchdgpfcd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~(u1\_struct\_0~(k3\_facirc\_2~X0~X1~X2))~(k3\_msafree2~(k3\_facirc\_2~\\
X0~X1~X2))){\unicdbdjdcd}((X3=k5\_facirc\_2~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_partfun1~\\
X4~k5\_numbers)))){\unicdcdcdhd}((X3=k1\_funct\_1~X4~X0){\unicdcdcdhd}((k1\_funct\_1~X4~k6\_numbers=\\
k4\_tarski~k1\_xboole\_0~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k7\_margrel1)){\unicdcdcdhd}({\unicdcdadad} X5 .  (v7\_ordinal1~\\
X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (X6=k1\_funct\_1~X4~X5){\unicdbdjdcd}(k1\_funct\_1~X4~(k1\_nat\_1~\\
X5~np\_\_1)=k17\_facirc\_1~(k1\_funct\_1~X1~(k1\_nat\_1~X5~np\_\_1))~(k1\_funct\_1~\\
X2~(k1\_nat\_1~X5~np\_\_1))~X6))))))))))\end{array}
\label{hyp:egfdpfggbgdgjgchdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v3\_msualg\_1~\\
X3~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}((v4\_msafree2~X3~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_circcomb~X3~(k3\_facirc\_2~X0~X1~X2)){\unicdcdcdhd}((v6\_circcomb~X3~(k3\_facirc\_2~\\
X0~X1~X2)){\unicdcdcdhd}(l3\_msualg\_1~X3~(k3\_facirc\_2~X0~X1~X2)))))){\unicdbdjdcd}((X3=k4\_facirc\_2~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_partfun1~X4~k5\_numbers)))){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}\\
(v1\_partfun1~X5~k5\_numbers)))){\unicdcdcdhd}({\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}\\
((v4\_relat\_1~X6~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~\\
k5\_numbers)))){\unicdcdcdhd}((k3\_facirc\_2~X0~X1~X2=k1\_funct\_1~X4~X0){\unicdcdcdhd}((X3=\\
k1\_funct\_1~X5~X0){\unicdcdcdhd}((k1\_funct\_1~X4~k6\_numbers=k5\_circcomb~(k1\_margrel1~\\
k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k7\_margrel1)~\\
k1\_xboole\_0){\unicdcdcdhd}((k1\_funct\_1~X5~k6\_numbers=k7\_circcomb~k1\_xboole\_0~\\
k6\_margrel1~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~k6\_numbers~\\
k6\_margrel1)~k7\_margrel1)~k1\_xboole\_0){\unicdcdcdhd}((k1\_funct\_1~X6~k6\_numbers=\\
k4\_tarski~k1\_xboole\_0~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k7\_margrel1)){\unicdcdcdhd}({\unicdcdadad} X7 .  (v7\_ordinal1~\\
X7){\unicdbdjdcd}({\unicdcdadad} X8 .  ((\preoh v2\_struct\_0~X8){\unicdcdcdhd}(l1\_msualg\_1~X8)){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
((v4\_msualg\_1~X9~X8){\unicdcdcdhd}(l3\_msualg\_1~X9~X8)){\unicdbdjdcd}({\unicdcdadad} X10 .  ((X8=\\
k1\_funct\_1~X4~X7){\unicdcdcdhd}((X9=k1\_funct\_1~X5~X7){\unicdcdcdhd}(X10=k1\_funct\_1~X6~X7))){\unicdbdjdcd}\\
((k1\_funct\_1~X4~(k1\_nat\_1~X7~np\_\_1)=k2\_circcomb~X8~(k19\_facirc\_1~\\
(k1\_funct\_1~X1~(k1\_nat\_1~X7~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X7~\\
np\_\_1))~X10)){\unicdcdcdhd}((k1\_funct\_1~X5~(k1\_nat\_1~X7~np\_\_1)=k3\_circcomb~\\
X8~(k19\_facirc\_1~(k1\_funct\_1~X1~(k1\_nat\_1~X7~np\_\_1))~(k1\_funct\_1~\\
X2~(k1\_nat\_1~X7~np\_\_1))~X10)~X9~(k20\_facirc\_1~(k1\_funct\_1~X1~(k1\_nat\_1~\\
X7~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X7~np\_\_1))~X10)){\unicdcdcdhd}(k1\_funct\_1~\\
X6~(k1\_nat\_1~X7~np\_\_1)=k17\_facirc\_1~(k1\_funct\_1~X1~(k1\_nat\_1~X7~\\
np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X7~np\_\_1))~X10)))))))))))))))))))\end{array}
\label{hyp:egedpfggbgdgjgchdgpfcd}
\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}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfggbgdgjgchdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((k3\_facirc\_2~k6\_numbers~X0~X1=k5\_circcomb~(k1\_margrel1~\\
k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k7\_margrel1)~\\
k1\_xboole\_0){\unicdcdcdhd}((k4\_facirc\_2~k6\_numbers~X0~X1=k7\_circcomb~k1\_xboole\_0~\\
k6\_margrel1~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~k6\_numbers~\\
k6\_margrel1)~k7\_margrel1)~k1\_xboole\_0){\unicdcdcdhd}(k5\_facirc\_2~k6\_numbers~\\
X0~X1=k4\_tarski~k1\_xboole\_0~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k7\_margrel1)))))\end{array}$$
\end{theorem}
\end{document}
