\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{t40\_sprect\_3 (TMb2MB85c9xC7PSV8hDbMSXXWJaU6XHLxpw)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_6 : {{\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 $ np\_\_2 : {\iota}$ be given.
Let $ v1\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_goboard5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_sprect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_goboard9 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_6~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~X0){\unicdcdcdhd}(\\
(v1\_goboard5~X0){\unicdcdcdhd}((v1\_sprect\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))))))){\unicdbdjdcd}((k2\_goboard9~X0=ReplSep~(toset~\\
({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~\\
({\uniddcgcg} X1 : \iota .  \preoh (r1\_xxreal\_0~(k6\_pscomp\_1~(k3\_topreal1~np\_\_2~X0))~\\
(k17\_euclid~X1)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X1)~(k8\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~(k9\_pscomp\_1~(k3\_topreal1~\\
np\_\_2~X0))~(k18\_euclid~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X1)~(k7\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0))))))~({\uniddcgcg} X1 : \iota .  X1)){\unicdcdcdhd}(k3\_goboard9~X0=\\
ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))~({\uniddcgcg} X1 : \iota .  (\preoh r1\_xxreal\_0~(k17\_euclid~X1)~(k6\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0))){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k8\_pscomp\_1~(k3\_topreal1~\\
np\_\_2~X0))~(k17\_euclid~X1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k18\_euclid~X1)~(k9\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0))){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k7\_pscomp\_1~(k3\_topreal1~\\
np\_\_2~X0))~(k18\_euclid~X1)))))~({\uniddcgcg} X1 : \iota .  X1)))\end{array}
\label{hyp:ehddhdpfdhahchfgdgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdhahchfgdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_6~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}((v1\_topreal1~X0){\unicdcdcdhd}((v2\_topreal1~X0){\unicdcdcdhd}(\\
(v1\_goboard5~X0){\unicdcdcdhd}((v1\_sprect\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}((\preoh (r1\_xxreal\_0~(k6\_pscomp\_1~(k3\_topreal1~\\
np\_\_2~X0))~(k17\_euclid~X1)){\unicdcdcdhd}((r1\_xxreal\_0~(k17\_euclid~X1)~(k8\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0))){\unicdcdcdhd}((r1\_xxreal\_0~(k9\_pscomp\_1~(k3\_topreal1~\\
np\_\_2~X0))~(k18\_euclid~X1)){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X1)~(k7\_pscomp\_1~\\
(k3\_topreal1~np\_\_2~X0)))))){\unicdbdjdcd}(X1 \in k2\_goboard9~X0)))\end{array}$$
\end{theorem}
\end{document}
