\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\_pralg\_1 (TMHuqbZ4wywwp9TWM7kbDLVj6w5Q3Wgv59P)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_pralg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}\\
((v3\_unialg\_1~X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdcdcdhd}(\\
(\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1)))))){\unicdbdjdcd}((r1\_unialg\_2~X0~X1){\unicdbdjdcd}(r1\_unialg\_2~\\
X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~(k4\_partfun1~(k3\_finseq\_2~\\
X0)~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_unialg\_1~X0~X1=g1\_unialg\_1~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_unialg\_1~X0){\unicdbdjdcd}(m2\_finseq\_1~(u1\_unialg\_1~X0)~(k4\_partfun1~\\
(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_unialg\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpffhogjgbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X1)){\unicdbdjdcd}\\
((v1\_funct\_1~(k6\_pralg\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k6\_pralg\_1~X0~\\
X1)~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~X1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k6\_pralg\_1~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
X1~X0))))))\end{array}
\label{hyp:egehpflggdpfahchbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}\\
((v3\_unialg\_1~X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdcdcdhd}(\\
(\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1)))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_pralg\_1~X0~X1)){\unicdcdcdhd}\\
((v1\_unialg\_1~(k5\_pralg\_1~X0~X1)){\unicdcdcdhd}((v2\_unialg\_1~(k5\_pralg\_1~\\
X0~X1)){\unicdcdcdhd}((v3\_unialg\_1~(k5\_pralg\_1~X0~X1)){\unicdcdcdhd}((v4\_unialg\_1~(k5\_pralg\_1~\\
X0~X1)){\unicdcdcdhd}(l1\_unialg\_1~(k5\_pralg\_1~X0~X1)))))))\end{array}
\label{hyp:egehpflgfdpfahchbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}((r1\_unialg\_2~X0~X1){\unicdbdjdcd}(k5\_pralg\_1~X0~\\
X1=g1\_unialg\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~\\
(k4\_pralg\_1~X0~X1))))\end{array}
\label{hyp:egfdpfahchbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_unialg\_1~X0){\unicdbdjdcd}((v1\_unialg\_1~X0){\unicdbdjdcd}(X0=g1\_unialg\_1~\\
(u1\_struct\_0~X0)~(u1\_unialg\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpffhogjgbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfahchbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}((r1\_unialg\_2~X0~X1){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_pralg\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))){\unicdcdcdhd}((v1\_funct\_2~\\
(k6\_pralg\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~(\\
k5\_pralg\_1~X0~X1))~(u1\_struct\_0~(k5\_pralg\_1~X1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
(k6\_pralg\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~(k5\_pralg\_1~X0~X1))~(u1\_struct\_0~(k5\_pralg\_1~\\
X1~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
