\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}
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\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{t11\_gfacirc2 (TMNwH1EErtBXWZRwczSMPQgs9bV64qjHb9r)}
\maketitle
Let $ v7\_ordinal1 : {{\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 $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_gfacirc2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k14\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_gfacirc1 : {{\iota}{\unicdbdjdcd}{{\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 $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\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 $ k7\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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.
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}((k1\_gfacirc2~(k1\_nat\_1~\\
X0~np\_\_1)~X1~X2=k2\_circcomb~(k1\_gfacirc2~X0~X1~X2)~(k13\_gfacirc1~\\
(k1\_funct\_1~X1~(k1\_nat\_1~X0~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X0~\\
np\_\_1))~(k3\_gfacirc2~X0~X1~X2))){\unicdcdcdhd}((k2\_gfacirc2~(k1\_nat\_1~X0~np\_\_1)~\\
X1~X2=k3\_circcomb~(k1\_gfacirc2~X0~X1~X2)~(k13\_gfacirc1~(k1\_funct\_1~\\
X1~(k1\_nat\_1~X0~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X0~np\_\_1))~(k3\_gfacirc2~\\
X0~X1~X2))~(k2\_gfacirc2~X0~X1~X2)~(k14\_gfacirc1~(k1\_funct\_1~X1~(k1\_nat\_1~\\
X0~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X0~np\_\_1))~(k3\_gfacirc2~X0~X1~\\
X2))){\unicdcdcdhd}(k3\_gfacirc2~(k1\_nat\_1~X0~np\_\_1)~X1~X2=k9\_gfacirc1~(k1\_funct\_1~\\
X1~(k1\_nat\_1~X0~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X0~np\_\_1))~(k3\_gfacirc2~\\
X0~X1~X2))))))\end{array}
\label{hyp:ehhdpfhgggbgdgjgchdgcd}
\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}(((v1\_relat\_1~(k3\_msafree2~\\
X0)){\unicdcdcdhd}(v1\_relat\_1~(k3\_msafree2~X1))){\unicdbdjdcd}(v1\_relat\_1~(k3\_msafree2~\\
(k2\_circcomb~X0~X1)))))\end{array}
\label{hyp:ehddpfggbgdgjgchdgpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  v1\_relat\_1~(k3\_msafree2~(k13\_gfacirc1~\\
X0~X1~X2))\end{array}
\label{hyp:ehddcdpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\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}((k1\_gfacirc2~k6\_numbers~X0~X1=k5\_circcomb~(k1\_margrel1~\\
k6\_margrel1~(k4\_finseq\_2~k6\_numbers~k6\_margrel1)~k7\_margrel1)~\\
k1\_xboole\_0){\unicdcdcdhd}((k2\_gfacirc2~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}(k3\_gfacirc2~k6\_numbers~\\
X0~X1=k4\_tarski~k1\_xboole\_0~(k1\_margrel1~k6\_margrel1~(k4\_finseq\_2~\\
k6\_numbers~k6\_margrel1)~k7\_margrel1)))))\end{array}
\label{hyp:ehcdpfhgggbgdgjgchdgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ((X0~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k1\_nat\_1~X1~np\_\_1))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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}((\preoh v2\_struct\_0~(k1\_gfacirc2~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k1\_gfacirc2~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k1\_gfacirc2~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k1\_gfacirc2~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k1\_gfacirc2~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k1\_gfacirc2~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k1\_gfacirc2~X0~X1~X2))))))))\end{array}
\label{hyp:egehpflgbdpfhgggbgdgjgchdgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k13\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k13\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k13\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k13\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k13\_gfacirc1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k13\_gfacirc1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k13\_gfacirc1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgbdddpfhgggbgdgjgchdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_xboole\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0))\end{array}
\label{hyp:dgdgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_relat\_1}~{X0}})}}}\label{hyp:dgdgbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_funct\_1}~{X0}})}}}\label{hyp:dgdgbdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfhgggbgdgjgchdgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}(v1\_relat\_1~(k3\_msafree2~\\
(k1\_gfacirc2~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
