\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{t9\_gfacirc2 (TMTBgRNcWYGcLqx3pKEUpQpCTcE9U9TL94A)}
\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\_xboole\_0 : {{\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\_circcomb : {{\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 $ 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}(k3\_msafree2~(k2\_circcomb~\\
X0~X1)=k2\_xboole\_0~(k3\_msafree2~X0)~(k3\_msafree2~X1)))\end{array}
\label{hyp:ehcdhdpfggbgdgjgchdgpfbd}
\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}
\begin{theorem}\label{thm:ehjdpfhgggbgdgjgchdgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~X2))){\unicdbdjdcd}(k3\_msafree2~(k1\_gfacirc2~\\
(k1\_nat\_1~X0~np\_\_1)~X1~X2)=k2\_xboole\_0~(k3\_msafree2~(k1\_gfacirc2~\\
X0~X1~X2))~(k3\_msafree2~(k13\_gfacirc1~(k1\_funct\_1~X1~(k1\_nat\_1~\\
X0~np\_\_1))~(k1\_funct\_1~X2~(k1\_nat\_1~X0~np\_\_1))~(k3\_gfacirc2~X0~X1~\\
X2))))))\end{array}$$
\end{theorem}
\end{document}
