\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{t10\_pralg\_3 (TMRADHbkqi3ui3PMDUk2GjSizRqt8TpiJ7r)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_pralg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pralg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_pralg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k14\_pralg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_pralg\_2~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u4\_struct\_0~X1)){\unicdbdjdcd}((k1\_msualg\_1~X1~X4=k1\_xboole\_0){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_pralg\_3~X1~(k14\_pralg\_2~X0~X1~X3)~X4)~X2=k1\_pralg\_3~X1~(k5\_pralg\_2~\\
X0~X1~X3~X2)~X4))))))\end{array}
\label{hyp:ehjdpfahchbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pralg\_2~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X1)){\unicdbdjdcd}((k1\_msualg\_1~\\
X1~X3=k1\_xboole\_0){\unicdbdjdcd}(k1\_pralg\_3~X1~(k14\_pralg\_2~X0~X1~X2)~X3 \in k1\_funct\_2~\\
X0~(k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~X0))~\\
({\uniddcgcg} X4 : \iota .  True)~({\uniddcgcg} X4 : \iota .  k4\_msualg\_1~X1~X3~(k5\_pralg\_2~\\
X0~X1~X2~X4)))))))))\end{array}
\label{hyp:ehidpfahchbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((k9\_xtuple\_0~X0=k9\_xtuple\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X0~X2=k1\_funct\_1~\\
X1~X2))){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_pralg\_2~X3~X1~X0)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k1\_pralg\_3~X0~(k14\_pralg\_2~X1~X0~X3)~X2)){\unicdcdcdhd}(v1\_funct\_1~\\
(k1\_pralg\_3~X0~(k14\_pralg\_2~X1~X0~X3)~X2)))\end{array}
\label{hyp:ggdgddpfahchbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k1\_funct\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdcdcdhd}((X3=\\
X4){\unicdcdcdhd}((k9\_xtuple\_0~X4=X0){\unicdcdcdhd}(r1\_tarski~(k10\_xtuple\_0~X4)~X1)))))\end{array}
\label{hyp:egcdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfahchbgmghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v11\_struct\_0~X1){\unicdcdcdhd}(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_pralg\_2~\\
X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_relat\_1~X4){\unicdcdcdhd}(v1\_funct\_1~X4)){\unicdbdjdcd}(((k1\_msualg\_1~X1~X3=k1\_xboole\_0){\unicdcdcdhd}\\
((k9\_xtuple\_0~X4=X0){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X4~X5=k1\_pralg\_3~X1~(k5\_pralg\_2~X0~X1~X2~X5)~X3)))){\unicdbdjdcd}(X4=k1\_pralg\_3~\\
X1~(k14\_pralg\_2~X0~X1~X2)~X3))))))\end{array}$$
\end{theorem}
\end{document}
