\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{t71\_modelc\_3 (TMdajQywZttpwahaWxwvXBswLsGQAepAawV)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k25\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k43\_modelc\_2 : {\iota}$ be given.
Let $ v1\_modelc\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_modelc\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ r7\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r8\_modelc\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k14\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k8\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_modelc\_2 : {\iota}$ be given.
Let $ k13\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k48\_modelc\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u3\_modelc\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_modelc\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k2\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(v1\_xboole\_0~\\
X1)\end{array}
\label{hyp:chdgcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X1=\\
X1)\end{array}
\label{hyp:jgegfgngahpgehfgogdgfgpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}\\
(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k1\_modelc\_3~X0))){\unicdcdcdhd}((m1\_subset\_1~X2~(k1\_zfmisc\_1~(k1\_modelc\_3~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k1\_modelc\_3~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g1\_modelc\_3~X0~X1~X2~X3=g1\_modelc\_3~\\
X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
m1\_subset\_1~(k8\_modelc\_3~X0)~(k1\_zfmisc\_1~(k1\_modelc\_3~X0)))\end{array}
\label{hyp:egehpflgidpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}\\
((v1\_modelc\_3~X1~X0){\unicdcdcdhd}(l1\_modelc\_3~X1~X0))){\unicdbdjdcd}(m1\_subset\_1~(k14\_modelc\_3~\\
X0~X1)~(k1\_zfmisc\_1~k9\_modelc\_2))\end{array}
\label{hyp:egehpflgbdedpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_modelc\_3~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k13\_modelc\_3~X0~X1)~(k1\_zfmisc\_1~k9\_modelc\_2))\end{array}
\label{hyp:egehpflgbdddpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
(v1\_modelc\_3~(k11\_modelc\_3~X0)~X0){\unicdcdcdhd}((v3\_modelc\_3~(k11\_modelc\_3~\\
X0)~X0){\unicdcdcdhd}(l1\_modelc\_3~(k11\_modelc\_3~X0)~X0)))\end{array}
\label{hyp:egehpflgbdbdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k9\_modelc\_2)){\unicdbdjdcd}(k48\_modelc\_2~\\
X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  (v1\_modelc\_2~X1){\unicdcdcdhd}(m2\_finseq\_1~\\
X1~k5\_numbers)))~({\uniddcgcg} X1 : \iota .  {\unicdcdaddd} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(\\
m2\_finseq\_1~X2~k5\_numbers)){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}(X1=k6\_modelc\_2~X2)))~\\
({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:eggdfdpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~k9\_modelc\_2)){\unicdbdjdcd}((r8\_modelc\_2~X0~\\
X1){\unicdbdjded}({\unicdcdadad} X2 .  ((v1\_modelc\_2~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~k5\_numbers)){\unicdbdjdcd}\\
((X2 \in X1){\unicdbdjdcd}(r7\_modelc\_2~X0~X2)))))\end{array}
\label{hyp:eggdedpfngpgegfgmgdgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_3~X1~X0){\unicdcdcdhd}(l1\_modelc\_3~X1~X0)){\unicdbdjdcd}(k14\_modelc\_3~\\
X0~X1=k2\_xboole\_0~(k4\_subset\_1~(k1\_modelc\_3~X0)~(u1\_modelc\_3~\\
X0~X1)~(u2\_modelc\_3~X0~X1))~(k48\_modelc\_2~(k13\_modelc\_3~X0~(u3\_modelc\_3~\\
X0~X1)))))\end{array}
\label{hyp:egcdcdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_modelc\_3~X0))){\unicdbdjdcd}(\\
k13\_modelc\_3~X0~X1=X1))\end{array}
\label{hyp:egcdbdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
k11\_modelc\_3~X0=g1\_modelc\_3~X0~(k7\_modelc\_3~X0)~(k7\_modelc\_3~\\
X0)~(k8\_modelc\_3~X0))\end{array}
\label{hyp:egbdhdpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
k8\_modelc\_3~X0=k1\_tarski~X0)\end{array}
\label{hyp:egbdedpfngpgegfgmgdgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_2~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
k7\_modelc\_3~X0=k1\_xboole\_0)\end{array}
\label{hyp:egbdddpfngpgegfgmgdgpfdd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_modelc\_2~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}\\
(l1\_modelc\_3~X1~X0)){\unicdbdjdcd}((v1\_modelc\_3~X1~X0){\unicdbdjdcd}(X1=g1\_modelc\_3~X0~\\
(u1\_modelc\_3~X0~X1)~(u2\_modelc\_3~X0~X1)~(u3\_modelc\_3~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfngpgegfgmgdgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehhdbdpfngpgegfgmgdgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k25\_modelc\_2~k43\_modelc\_2)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_modelc\_2~X1){\unicdcdcdhd}((v5\_modelc\_3~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers))){\unicdbdjdcd}\\
((r7\_modelc\_2~X0~(k6\_modelc\_2~X1)){\unicdbdjdcd}(r8\_modelc\_2~X0~(k14\_modelc\_3~\\
X1~(k11\_modelc\_3~X1)))))\end{array}$$
\end{theorem}
\end{document}
