\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=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t4\_ami\_wstd (TMPKPNyaQRkPoUNMZnsqznRZVWEtdruMdkj)}
\maketitle
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\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_ami\_wstd : {{\iota}{\unicdbdjdcd}{{\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 $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_amistd\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ami\_wstd : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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\_extpro\_1~X1~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k5\_numbers))))){\unicdbdjdcd}\\
((v3\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m2\_subset\_1~\\
X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X3~X4){\unicdbdjded}(r1\_ami\_wstd~X0~X1~(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~X2~X3)~(k3\_funct\_2~k5\_numbers~k5\_numbers~\\
X2~X4))))){\unicdbdjded}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((k3\_funct\_2~k5\_numbers~k5\_numbers~X2~(k2\_nat\_1~X3~np\_\_1) \in k3\_amistd\_1~\\
X0~X1~(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k3\_funct\_2~k5\_numbers~k5\_numbers~\\
X2~X4 \in k3\_amistd\_1~X0~X1~(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~X3)){\unicdbdjdcd}\\
(r1\_xxreal\_0~X3~X4)))))))))\end{array}
\label{hyp:ehddpfbgngjgpfhhdheheg}
\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}(l1\_extpro\_1~X1~X0)))){\unicdbdjdcd}\\
((v2\_ami\_wstd~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k5\_numbers))))){\unicdcdcdhd}((v3\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X3~X4){\unicdbdjded}\\
(r1\_ami\_wstd~X0~X1~(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~X3)~(k3\_funct\_2~\\
k5\_numbers~k5\_numbers~X2~X4)))))))))\end{array}
\label{hyp:egddpfbgngjgpfhhdheheg}
\end{equation}
\begin{theorem}\label{thm:ehedpfbgngjgpfhhdheheg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_setfam\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0)))){\unicdbdjdcd}\\
((v2\_ami\_wstd~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k5\_numbers))))){\unicdcdcdhd}((v3\_funct\_2~X2~k5\_numbers~k5\_numbers){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k3\_funct\_2~\\
k5\_numbers~k5\_numbers~X2~(k2\_nat\_1~X3~np\_\_1) \in k3\_amistd\_1~X0~X1~\\
(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k3\_funct\_2~k5\_numbers~k5\_numbers~\\
X2~X4 \in k3\_amistd\_1~X0~X1~(k3\_funct\_2~k5\_numbers~k5\_numbers~X2~X3)){\unicdbdjdcd}\\
(r1\_xxreal\_0~X3~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
