\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t10\_scmringi (TMKNwSp9eTFZ7hjTS4JGrPWGMApsHURwZXc)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_scmringi : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_scm\_inst : {\iota}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_enumset1 : {{\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\_\_7 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_scm\_inst}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhdgngpfjgogdheh}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(k1\_scmringi~\\
X0=k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k2\_xboole\_0~(k1\_tarski~\\
(k3\_xtuple\_0~k6\_numbers~k1\_xboole\_0~k1\_xboole\_0))~(ReplSep3~\\
(toset~({\uniddcgcg} X1 : \iota .  m2\_subset\_1~X1~k4\_ordinal1~(k7\_card\_1~np\_\_8)))~\\
({\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 k2\_enumset1~np\_\_1~np\_\_2~\\
np\_\_3~np\_\_4)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~\\
X1~k1\_xboole\_0~(k2\_finseq\_4~k2\_scm\_inst~X2~X3))))~(ReplSep~(toset~\\
({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k5\_numbers))~({\uniddcgcg} X1 : \iota .  True)~(\\
{\uniddcgcg} X1 : \iota .  k3\_xtuple\_0~np\_\_6~(k12\_finseq\_1~k5\_numbers~X1)~k1\_xboole\_0)))~\\
(ReplSep2~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k5\_numbers))~({\uniddcgcg} X1 : \\
\iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  True)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k3\_xtuple\_0~np\_\_7~\\
(k12\_finseq\_1~k5\_numbers~X1)~(k12\_finseq\_1~k2\_scm\_inst~X2))))~\\
(ReplSep2~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~k2\_scm\_inst))~({\uniddcgcg} X1 : \\
\iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(u1\_struct\_0~X0)))~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  True)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k3\_xtuple\_0~np\_\_5~\\
k1\_xboole\_0~(k10\_finseq\_1~X1~X2))))\end{array}
\label{hyp:egbdpfdhdgngchjgoghgjg}
\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}
\begin{theorem}\label{thm:ehbdadpfdhdgngchjgoghgjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}(k3\_xtuple\_0~np\_\_6~(k12\_finseq\_1~\\
k5\_numbers~X1)~k1\_xboole\_0 \in k1\_scmringi~X0))\end{array}$$
\end{theorem}
\end{document}
