\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{t27\_mfold\_2 (TMVnkhdz1DJaK78Q2ZafZFh2j4WtBgK1iPw)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v3\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_mfold\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_rlvect\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rlvect\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Let $ v1\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_matrtop1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~(k15\_euclid~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((v1\_rlvect\_3~X2~(k15\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}(\preoh (k1\_card\_1~X2=k10\_binop\_2~\\
X0~np\_\_1){\unicdcdcdhd}(k2\_struct\_0~(k1\_rlvect\_3~(k15\_euclid~X0)~X2)=k2\_mfold\_2~\\
X0~X1~(k4\_struct\_0~(k15\_euclid~X0)))))))\end{array}
\label{hyp:ehcdgdpfngggpgmgegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_rlvect\_3~X1~(k15\_euclid~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_rlvect\_3~X2~(k15\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}(\preoh (k1\_card\_1~\\
X1=k1\_card\_1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_matrix\_1~X3~(u1\_struct\_0~k2\_vectsp\_1)~\\
X0~X0){\unicdbdjdcd}(\preoh (v1\_matrix\_6~X3~X0~k2\_vectsp\_1){\unicdcdcdhd}(k7\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))~(u1\_struct\_0~(k15\_euclid~X0))~(k3\_matrtop1~X0~\\
X0~X3)~(k2\_struct\_0~(k1\_rlvect\_3~(k15\_euclid~X0)~X1))=k2\_struct\_0~\\
(k1\_rlvect\_3~(k15\_euclid~X0)~X2)))))))\end{array}
\label{hyp:ehcdcdpfngbgehchehpgahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v1\_matrix\_6~X1~X0~k2\_vectsp\_1){\unicdcdcdhd}\\
(m1\_matrix\_1~X1~(u1\_struct\_0~k2\_vectsp\_1)~X0~X0))){\unicdbdjdcd}((v1\_funct\_1~\\
(k3\_matrtop1~X0~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k3\_matrtop1~X0~X0~X1)~(u1\_struct\_0~\\
(k15\_euclid~X0))~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(v3\_tops\_2~(\\
k3\_matrtop1~X0~X0~X1)~(k15\_euclid~X0)~(k15\_euclid~X0))))\end{array}
\label{hyp:ggdgbdddpfngbgehchehpgahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(m1\_matrix\_1~X2~(u1\_struct\_0~k2\_vectsp\_1)~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~\\
(k3\_matrtop1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k3\_matrtop1~X0~X1~X2)~(u1\_struct\_0~\\
(k15\_euclid~X0))~(u1\_struct\_0~(k15\_euclid~X1))){\unicdcdcdhd}(m1\_subset\_1~\\
(k3\_matrtop1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~X0))~(u1\_struct\_0~(k15\_euclid~X1)))))))\end{array}
\label{hyp:egehpflgddpfngbgehchehpgahbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfngggpgmgegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(\\
k15\_euclid~X0))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k4\_struct\_0~(k15\_euclid~X0)){\unicdcdcdhd}((X2{\unicdcdgdad}k4\_struct\_0~\\
(k15\_euclid~X0)){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u1\_struct\_0~(k15\_euclid~X0))~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
X0))~(u1\_struct\_0~(k15\_euclid~X0))))))){\unicdbdjdcd}(\preoh (v3\_tops\_2~X3~(k15\_euclid~\\
X0)~(k15\_euclid~X0)){\unicdcdcdhd}(k7\_relset\_1~(u1\_struct\_0~(k15\_euclid~X0))~\\
(u1\_struct\_0~(k15\_euclid~X0))~X3~(k2\_mfold\_2~X0~X1~(k4\_struct\_0~\\
(k15\_euclid~X0)))=k2\_mfold\_2~X0~X2~(k4\_struct\_0~(k15\_euclid~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
