\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{t1\_scmfsa\_2 (TMQH5xtw75nDpPochZgsvuTxeHyjFJX4XDt)}
\maketitle
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_scmfsa\_1 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_scmfsa\_i : {\iota}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_scmfsa\_1 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k4\_scmfsa\_1 : {\iota}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_scmfsa\_1 : {\iota}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{k5\_numbers} \in {k1\_scmfsa\_1}}\label{hyp:ehfdpfdhdgngggdhbgpfbd}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  ((m1\_subset\_1~X2~X1){\unicdcdcdhd}(((v1\_compos\_0~X3){\unicdcdcdhd}((v2\_compos\_0~\\
X3){\unicdcdcdhd}((v3\_compos\_0~X3){\unicdcdcdhd}(v5\_compos\_0~X3)))){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v1\_funct\_2~X4~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X1~X0))))){\unicdcdcdhd}(((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~X5~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X5){\unicdcdcdhd}(v1\_partfun1~X5~X0)))){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~\\
X3~(k1\_funct\_2~(k4\_card\_3~(k3\_relat\_1~X4~X5))~(k4\_card\_3~(k3\_relat\_1~\\
X4~X5)))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X3~(k1\_funct\_2~\\
(k4\_card\_3~(k3\_relat\_1~X4~X5))~(k4\_card\_3~(k3\_relat\_1~X4~X5)))))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  {\unicdcdadad} X10 .  {\unicdcdadad} X11 .  {\unicdcdadad} X12 .  \\
{\unicdcdadad} X13 .  (g1\_extpro\_1~X0~X1~X2~X3~X4~X5~X6=g1\_extpro\_1~X7~X8~X9~\\
X10~X11~X12~X13){\unicdbdjdcd}((X0=X7){\unicdcdcdhd}((X1=X8){\unicdcdcdhd}((X2=X9){\unicdcdcdhd}((X3=X10){\unicdcdcdhd}((X4=\\
X11){\unicdcdcdhd}((X5=X12){\unicdcdcdhd}(X6=X13))))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v5\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdggdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v3\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgfdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v2\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgedpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k2\_scmfsa\_i}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k2\_scmfsa\_i}})}}\label{hyp:ggdgddpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{l1\_memstr\_0}~{X1}}~{X0}})}{\unicdbdjdcd}{({{l2\_struct\_0}~{X1}})}}}}\label{hyp:egehpfmgbdpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_relat\_1~k5\_scmfsa\_1){\unicdcdcdhd}((v4\_relat\_1~k5\_scmfsa\_1~np\_\_3){\unicdcdcdhd}(\\
(v1\_funct\_1~k5\_scmfsa\_1){\unicdcdcdhd}(v1\_partfun1~k5\_scmfsa\_1~np\_\_3)))\end{array}
\label{hyp:egehpflgfdpfdhdgngggdhbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k4\_scmfsa\_1){\unicdcdcdhd}((v1\_funct\_2~k4\_scmfsa\_1~k1\_scmfsa\_1~\\
np\_\_3){\unicdcdcdhd}(m1\_subset\_1~k4\_scmfsa\_1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_scmfsa\_1~\\
np\_\_3))))\end{array}
\label{hyp:egehpflgedpfdhdgngggdhbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:egehpflgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k12\_scmfsa\_1){\unicdcdcdhd}((v1\_funct\_2~k12\_scmfsa\_1~k2\_scmfsa\_i~\\
(k1\_funct\_2~(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1))~\\
(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1)))){\unicdcdcdhd}(m1\_subset\_1~\\
k12\_scmfsa\_1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_scmfsa\_i~(k1\_funct\_2~\\
(k4\_card\_3~(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1))~(k4\_card\_3~\\
(k3\_relat\_1~k4\_scmfsa\_1~k5\_scmfsa\_1)))))))\end{array}
\label{hyp:egehpflgbdcdpfdhdgngggdhbgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k4\_struct\_0}~{X0}}={{u2\_struct\_0}~{X0}}})}}}\label{hyp:eggdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_scmfsa\_2=g1\_extpro\_1~np\_\_3~k1\_scmfsa\_1~(k1\_funct\_7~k5\_numbers~\\
k1\_scmfsa\_1)~k2\_scmfsa\_i~k4\_scmfsa\_1~k5\_scmfsa\_1~k12\_scmfsa\_1\end{array}
\label{hyp:egbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{{k1\_funct\_7}~{X0}}~{X1}}={X0}})}}}}\label{hyp:egbdpfggfhogdgehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((v1\_extpro\_1~X1~X0){\unicdbdjdcd}\\
(X1=g1\_extpro\_1~X0~(u1\_struct\_0~X1)~(u2\_struct\_0~X1)~(u1\_compos\_1~\\
X1)~(u1\_memstr\_0~X0~X1)~(u2\_memstr\_0~X0~X1)~(u1\_extpro\_1~X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpffgihehahchpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdhdgngggdhbgpfcd}
${{{k4\_struct\_0}~{k1\_scmfsa\_2}}={k5\_numbers}}$.
\end{theorem}
\end{document}
