\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{t10\_scm\_inst (TMQ4tUcMRhpRjFRrmD6WEpYzTwYV1bEwuQH)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_scm\_inst : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_scm\_inst : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_6 : {\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 $ 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.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}(\preoh (\preoh (X0 \in k1\_tarski~(\\
k3\_xtuple\_0~k1\_scm\_inst~k1\_xboole\_0~k1\_xboole\_0)){\unicdcdcdhd}(k4\_xtuple\_0~\\
X0=k6\_numbers)){\unicdcdcdhd}((\preoh (X0 \in ReplSep2~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~\\
X1~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~k5\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  X1=np\_\_6)~({\uniddcgcg} X1 : \iota .  \\
{\uniddcgcg} X2 : \iota .  k3\_xtuple\_0~X1~(k12\_finseq\_1~k5\_numbers~X2)~k1\_xboole\_0)){\unicdcdcdhd}\\
(k4\_xtuple\_0~X0=np\_\_6)){\unicdcdcdhd}((\preoh (X0 \in ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  \\
m1\_subset\_1~X1~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~k5\_numbers))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~\\
({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k2\_scm\_inst))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  X1 \in k7\_domain\_1~k5\_numbers~np\_\_7~np\_\_8)~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X1~(k12\_finseq\_1~k5\_numbers~\\
X2)~(k12\_finseq\_1~k2\_scm\_inst~X3))){\unicdcdcdhd}((k4\_xtuple\_0~X0=np\_\_7){\unicdcdcdid}\\
(k4\_xtuple\_0~X0=np\_\_8))){\unicdcdcdhd}(\preoh (X0 \in ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  \\
m1\_subset\_1~X1~(k7\_card\_1~np\_\_9)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~\\
({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k2\_scm\_inst))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  X1 \in k10\_domain\_1~k5\_numbers~np\_\_1~np\_\_2~np\_\_3~\\
np\_\_4~np\_\_5)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~\\
X1~k1\_xboole\_0~(k2\_finseq\_4~k2\_scm\_inst~X2~X3))){\unicdcdcdhd}(\preoh (k4\_xtuple\_0~\\
X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k4\_xtuple\_0~X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k4\_xtuple\_0~X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}\\
((k4\_xtuple\_0~X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}(k4\_xtuple\_0~X0{\unicdcdgdad}np\_\_5)))))))))\end{array}
\label{hyp:ehjdpfdhdgngpfjgogdheh}
\end{equation}
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}
\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}
\begin{array}{c}((v2\_xxreal\_0~np\_\_6){\unicdcdcdhd}(m2\_subset\_1~np\_\_6~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_6~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_6~k1\_numbers))\end{array}
\label{hyp:dhahdggdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_5){\unicdcdcdhd}(m2\_subset\_1~np\_\_5~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_5~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_5~k1\_numbers))\end{array}
\label{hyp:dhahdgfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(m2\_subset\_1~np\_\_0~k1\_numbers~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~np\_\_0~\\
k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_0~k1\_numbers))\end{array}
\label{hyp:dhahdgadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_7}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchhd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_6}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchgd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_5}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchfd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_4}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfched}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_3}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_2}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_1}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_8}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchidpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~X0)){\unicdbdjdcd}(k2\_compos\_0~X0~X1=k4\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdgedpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k4\_xtuple\_0}~{X0}}={{k1\_xtuple\_0}~{({{k1\_xtuple\_0}~{X0}})}}}}\label{hyp:eggdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfdhdgngpfjgogdheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_compos\_0~\\
k3\_scm\_inst~X0)~np\_\_8)\end{array}$$
\end{theorem}
\end{document}
