\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{t14\_fscirc\_2 (TMHGgg6wJgrdfYcSfbA1wNafhz2VY3ofxnc)}
\maketitle
Let $ k3\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_twoscomp : {\iota}$ be given.
Let $ k2\_twoscomp : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\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 $ k2\_circcomb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_fscirc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k4\_facirc\_1 : {\iota}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  ((\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 .  k3\_msafree2~(k3\_fscirc\_1~X0~\\
X1~X2)=k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp)~\\
(k4\_tarski~(k10\_finseq\_1~X1~X2)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~\\
X0~X2)~k3\_twoscomp)\end{array}
\label{hyp:ehbdcdpfggdhdgjgchdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~(k11\_finseq\_1~X0~\\
X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(k11\_finseq\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgjdpfggjgogdhfgbhpfbd}
\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 .  {\unicdcdadad} X2 .  v1\_finseq\_1~(k11\_finseq\_1~X0~\\
X1~X2)\end{array}
\label{hyp:ggdgbdbdpfggjgogdhfgbhpfbd}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (\preoh v2\_struct\_0~(k3\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k3\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k3\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_circcomb~(k3\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v2\_circcomb~(k3\_fscirc\_1~X0~X1~X2)){\unicdcdcdhd}((v3\_circcomb~(k3\_fscirc\_1~\\
X0~X1~X2)){\unicdcdcdhd}(l1\_msualg\_1~(k3\_fscirc\_1~X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgddpfggdhdgjgchdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k6\_fscirc\_1~X0~X1~X2=k4\_tarski~\\
(k11\_finseq\_1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp)~(k4\_tarski~\\
(k10\_finseq\_1~X1~X2)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X0~\\
X2)~k3\_twoscomp))~k4\_facirc\_1\end{array}
\label{hyp:eggdpfggdhdgjgchdgpfbd}
\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 .  k4\_fscirc\_1~X0~X1~X2=k2\_circcomb~\\
(k3\_fscirc\_1~X0~X1~X2)~(k5\_circcomb~k4\_facirc\_1~(k11\_finseq\_1~\\
(k4\_tarski~(k10\_finseq\_1~X0~X1)~k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~\\
X1~X2)~k2\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X0~X2)~k3\_twoscomp)))\end{array}
\label{hyp:egedpfggdhdgjgchdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfggdhdgjgchdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_msafree2~(k4\_fscirc\_1~X0~\\
X1~X2)=k2\_xboole\_0~(k1\_enumset1~(k4\_tarski~(k10\_finseq\_1~X0~X1)~\\
k3\_twoscomp)~(k4\_tarski~(k10\_finseq\_1~X1~X2)~k2\_twoscomp)~(k4\_tarski~\\
(k10\_finseq\_1~X0~X2)~k3\_twoscomp))~(k1\_tarski~(k6\_fscirc\_1~X0~\\
X1~X2))\end{array}$$
\end{theorem}
\end{document}
