\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{t20\_extpro\_1 (TMKD1YTPFTvSu1EnukfxUesyYRNCZutgXRy)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\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 $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ r1\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k6\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(\preoh v1\_setfam\_1~X2)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh \\
v2\_struct\_0~X3){\unicdcdcdhd}((v2\_memstr\_0~X3~X2){\unicdcdcdhd}((v3\_memstr\_0~X3~X2){\unicdcdcdhd}((\\
v3\_extpro\_1~X3~X2){\unicdcdcdhd}(l1\_extpro\_1~X3~X2))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X4~(u1\_compos\_1~\\
X3)){\unicdcdcdhd}(v1\_funct\_1~X4)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~\\
X5~(u1\_struct\_0~X3)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v5\_funct\_1~X5~(k2\_memstr\_0~\\
X2~X3)){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~X3)))))){\unicdbdjdcd}((r1\_compos\_1~\\
X3~X4~(k5\_memstr\_0~X2~X3~(k5\_extpro\_1~X2~X3~X4~X5~X0))){\unicdbdjdcd}(r1\_compos\_1~\\
X3~X4~(k5\_memstr\_0~X2~X3~(k5\_extpro\_1~X2~X3~X4~X5~X1))))))))))\end{array}
\label{hyp:ehbdjdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\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 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~X2)))){\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}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_compos\_1~X1~X2~(k5\_memstr\_0~X0~\\
X1~(k5\_extpro\_1~X0~X1~X2~X3~X4))){\unicdbdjdcd}(k6\_extpro\_1~X0~X1~X2~X3=k5\_extpro\_1~\\
X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:ehbdidpffgihehahchpgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpffgihehahchpgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(\preoh v1\_setfam\_1~X2)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh \\
v2\_struct\_0~X3){\unicdcdcdhd}((v2\_memstr\_0~X3~X2){\unicdcdcdhd}((v3\_memstr\_0~X3~X2){\unicdcdcdhd}((\\
v3\_extpro\_1~X3~X2){\unicdcdcdhd}(l1\_extpro\_1~X3~X2))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X4~(u1\_compos\_1~\\
X3)){\unicdcdcdhd}(v1\_funct\_1~X4)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v4\_relat\_1~\\
X5~(u1\_struct\_0~X3)){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v5\_funct\_1~X5~(k2\_memstr\_0~\\
X2~X3)){\unicdcdcdhd}(v1\_partfun1~X5~(u1\_struct\_0~X3)))))){\unicdbdjdcd}((r1\_compos\_1~\\
X3~X4~(k5\_memstr\_0~X2~X3~(k5\_extpro\_1~X2~X3~X4~X5~X0))){\unicdbdjdcd}(k5\_extpro\_1~\\
X2~X3~X4~X5~X1=k5\_extpro\_1~X2~X3~X4~X5~X0))))))))\end{array}$$
\end{theorem}
\end{document}
