\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{t3\_scm\_inst (TMQfFLNXB81fUHiBLzqsptjzKgQbmj1cq7U)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_scm\_inst : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_scm\_inst : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in X1){\unicdbdjded}(\preoh r1\_xxreal\_0~X1~X0)))\end{array}
\label{hyp:ehededpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_9){\unicdcdcdhd}(m2\_subset\_1~np\_\_9~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_9~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_9~k1\_numbers))\end{array}
\label{hyp:dhahdgjdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_8){\unicdcdcdhd}(m2\_subset\_1~np\_\_8~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_8~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_8~k1\_numbers))\end{array}
\label{hyp:dhahdgidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_7){\unicdcdcdhd}(m2\_subset\_1~np\_\_7~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_7~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_7~k1\_numbers))\end{array}
\label{hyp:dhahdghdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_9}}~{np\_\_8}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchjdpfchid}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_9}}~{np\_\_7}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchjdpfchhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k7\_domain\_1~X0~X1~X2=k2\_tarski~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k7\_card\_1}~{X0}}={{k6\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_scm\_inst}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k6\_card\_1}~{X0}}={X0}})}}}\label{hyp:eggdpfdgbgchegpfbd}
\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 .  k3\_xtuple\_0~X0~X1~X2=k4\_tarski~\\
(k4\_tarski~X0~X1)~X2\end{array}
\label{hyp:egedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdid}(X3 \in X1)))\end{array}
\label{hyp:egddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k2\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3=X0){\unicdcdcdid}(X3=X1)))\end{array}
\label{hyp:egcdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k3\_scm\_inst=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k1\_tarski~\\
(k3\_xtuple\_0~k1\_scm\_inst~k1\_xboole\_0~k1\_xboole\_0))~(ReplSep2~\\
(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X0 : \\
\iota .  toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k5\_numbers))~({\uniddcgcg} X0 : \iota .  \\
{\uniddcgcg} X1 : \iota .  X0=np\_\_6)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~X0~\\
(k12\_finseq\_1~k5\_numbers~X1)~k1\_xboole\_0)))~(ReplSep3~(toset~\\
({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X0 : \iota .  \\
toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k5\_numbers))~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \\
\iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X0 : \\
\iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  X0 \in k7\_domain\_1~k5\_numbers~np\_\_7~\\
np\_\_8)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k3\_xtuple\_0~X0~(k12\_finseq\_1~\\
k5\_numbers~X1)~(k12\_finseq\_1~k2\_scm\_inst~X2))))~(ReplSep3~(toset~\\
({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X0 : \iota .  \\
toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k2\_scm\_inst))~({\uniddcgcg} X0 : \iota .  \\
{\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_scm\_inst))~(\\
{\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  X0 \in k10\_domain\_1~k5\_numbers~\\
np\_\_1~np\_\_2~np\_\_3~np\_\_4~np\_\_5)~({\uniddcgcg} X0 : \iota .  {\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  k3\_xtuple\_0~X0~k1\_xboole\_0~(k2\_finseq\_4~k2\_scm\_inst~X1~X2)))\end{array}
\label{hyp:egcdpfdhdgngpfjgogdheh}
\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}
{{\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:ehddpfdhdgngpfjgogdheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~k2\_scm\_inst){\unicdbdjdcd}((X0 \in k7\_domain\_1~k5\_numbers~np\_\_7~\\
np\_\_8){\unicdbdjdcd}(k3\_xtuple\_0~X0~(k12\_finseq\_1~k5\_numbers~X1)~(k12\_finseq\_1~\\
k2\_scm\_inst~X2) \in k3\_scm\_inst)))\end{array}$$
\end{theorem}
\end{document}
