\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\_amistd\_5 (TMdMMg7rzhD637TLfUty7MyP9x8bvb2y1bi)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v3\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_amistd\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\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 $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_amistd\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_compos\_0~X0){\unicdcdcdhd}((v2\_compos\_0~\\
X0){\unicdcdcdhd}(v3\_compos\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}(k5\_compos\_0~\\
X0~X1~k6\_numbers=X1))\end{array}
\label{hyp:ehddpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k2\_xcmplx\_0}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehbdpfbgchjgehigng}
\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 .  (l1\_compos\_1~X0){\unicdbdjdcd}((v1\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v2\_compos\_0~(u1\_compos\_1~X0)){\unicdcdcdhd}((v3\_compos\_0~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}(v5\_compos\_0~(u1\_compos\_1~X0)))))\end{array}
\label{hyp:egehpffhbdpfdgpgngahpgdhpfbd}
\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}{\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}((v3\_extpro\_1~X1~X0){\unicdcdcdhd}\\
(l1\_extpro\_1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_compos\_1~\\
X1)){\unicdbdjdcd}((v1\_amistd\_5~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~\\
X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v5\_funct\_1~X5~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~X1)))))){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~\\
X1)~(k2\_extpro\_1~X0~X1~(k5\_compos\_0~(u1\_compos\_1~X1)~X2~(k2\_xcmplx\_0~\\
X3~X4))~(k9\_memstr\_0~X0~X1~X5~X4))~(k9\_memstr\_0~X0~X1~(k2\_extpro\_1~\\
X0~X1~(k5\_compos\_0~(u1\_compos\_1~X1)~X2~X3)~X5)~X4))))))))\end{array}
\label{hyp:egbdpfbgngjgdhehegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~X1=k2\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihdgngahmgihpfad}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_compos\_0}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgcdpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_extpro\_1~X1~X0){\unicdcdcdhd}\\
((v2\_amistd\_5~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_compos\_1~X1)){\unicdbdjdcd}(v1\_amistd\_5~X2~X0~X1))\end{array}
\label{hyp:dgdgcdpfbgngjgdhehegpffd}
\end{equation}
\begin{theorem}\label{thm:ehedpfbgngjgdhehegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_setfam\_1~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_memstr\_0~X2~X1){\unicdcdcdhd}((v3\_memstr\_0~\\
X2~X1){\unicdcdcdhd}((v3\_extpro\_1~X2~X1){\unicdcdcdhd}((v2\_amistd\_5~X2~X1){\unicdcdcdhd}(l1\_extpro\_1~\\
X2~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_compos\_1~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~(u1\_struct\_0~X2)){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v5\_funct\_1~X4~(k2\_memstr\_0~X1~X2)){\unicdcdcdhd}(v1\_partfun1~X4~(u1\_struct\_0~\\
X2)))))){\unicdbdjdcd}(r8\_pboole~(u1\_struct\_0~X2)~(k2\_extpro\_1~X1~X2~(k5\_compos\_0~\\
(u1\_compos\_1~X2)~X3~X0)~(k9\_memstr\_0~X1~X2~X4~X0))~(k9\_memstr\_0~X1~\\
X2~(k2\_extpro\_1~X1~X2~X3~X4)~X0))))))\end{array}$$
\end{theorem}
\end{document}
