\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{t24\_weddwitt (TMQX4W7s4MuU8Y5KbZgwBhmrJf9Nfgowt3V)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\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 $ k5\_weddwitt : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((\\
v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(u1\_struct\_0~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((\\
\preoh v6\_struct\_0~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k5\_weddwitt~\\
X0~X1)){\unicdcdcdhd}((v33\_algstr\_0~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v36\_algstr\_0~(\\
k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v3\_group\_1~\\
(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v4\_vectsp\_1~(k5\_weddwitt~X0~X1)){\unicdcdcdhd}((v5\_vectsp\_1~\\
(k5\_weddwitt~X0~X1)){\unicdcdcdhd}(l6\_algstr\_0~(k5\_weddwitt~X0~X1)))))))))))))\end{array}
\label{hyp:egehpflgfdpfhhfgegeghhjgeheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v6\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v36\_algstr\_0~X2){\unicdcdcdhd}\\
((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v3\_group\_1~\\
X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))))){\unicdbdjdcd}\\
((X2=k5\_weddwitt~X0~X1){\unicdbdjded}((u1\_struct\_0~X2=ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(u1\_struct\_0~X0)))~({\uniddcgcg} X3 : \iota .  k6\_algstr\_0~\\
X0~X3~X1=k6\_algstr\_0~X0~X1~X3)~({\uniddcgcg} X3 : \iota .  X3)){\unicdcdcdhd}((u1\_algstr\_0~\\
X2=k1\_realset1~(u1\_algstr\_0~X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}((u2\_algstr\_0~\\
X2=k1\_realset1~(u2\_algstr\_0~X0)~(u1\_struct\_0~X2)){\unicdcdcdhd}((k4\_struct\_0~\\
X2=k4\_struct\_0~X0){\unicdcdcdhd}(k5\_struct\_0~X2=k5\_struct\_0~X0))))))))\end{array}
\label{hyp:egfdpfhhfgegeghhjgeheh}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfhhfgegeghhjgeheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~\\
X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((X2 \in u1\_struct\_0~(k5\_weddwitt~X0~X1)){\unicdbdjded}(k6\_algstr\_0~X0~X2~X1=k6\_algstr\_0~\\
X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
