\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{t4\_scmfsa8b (TMQdKdhK4KMpZcYWcLtV86EsrBZS58pcdCG)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
X2~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~X3~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((k6\_memstr\_0~\\
X0~X1~X2=k6\_memstr\_0~X0~X1~X3){\unicdbdjdcd}(k8\_memstr\_0~X0~X1~X2=k8\_memstr\_0~\\
X0~X1~X3)))))\end{array}
\label{hyp:ehidadpfngfgngdhehchpfad}
\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}
{\preoh{{{v1\_xboole\_0}~{np\_\_3}}}}\label{hyp:dhahdgddpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~X0)))))){\unicdbdjdcd}(r8\_pboole~X0~X1~X1)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchidpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v3\_memstr\_0}~{k1\_scmfsa\_2}}~{np\_\_3}})}{\unicdcdcdhd}{({{{v1\_extpro\_1}~{k1\_scmfsa\_2}}~{np\_\_3}})}}\label{hyp:ggdgfdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k1\_scmfsa\_2){\unicdcdcdhd}((v2\_memstr\_0~k1\_scmfsa\_2~np\_\_3){\unicdcdcdhd}\\
(v1\_extpro\_1~k1\_scmfsa\_2~np\_\_3))\end{array}
\label{hyp:ggdgbdpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~\\
X0)))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
X2~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}((v1\_relat\_1~(k8\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k8\_memstr\_0~X0~X1~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k8\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}((v5\_funct\_1~(k8\_memstr\_0~X0~X1~X2)~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k8\_memstr\_0~X0~X1~X2)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:ggdgbdedpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\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}
{{({{{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}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_setfam\_1~X0)))\end{array}
\label{hyp:dgdgbdpfbgngjgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedpfdhdgngggdhbgidcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X3~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~\\
X3){\unicdcdcdhd}(v1\_afinsq\_1~X3))))))){\unicdbdjdcd}((k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~\\
X0=k6\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X1){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~\\
k1\_scmfsa\_2)~(k8\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X0)~(k8\_memstr\_0~\\
np\_\_3~k1\_scmfsa\_2~X1))))))\end{array}$$
\end{theorem}
\end{document}
