\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{t83\_sprect\_1 (TMQf7SJNhzYJ3EDjW92pW5pj9XHxqySidbN)}
\maketitle
Let $ v1\_sprect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_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 $ np\_\_2 : {\iota}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k20\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_sprect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
(k20\_pscomp\_1~(k3\_topreal1~np\_\_2~(k1\_sprect\_1~X0))=k11\_pscomp\_1~\\
X0)\end{array}
\label{hyp:ehhdgdpfdhahchfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_compts\_1~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))){\unicdbdjdcd}\\
(k19\_pscomp\_1~(k3\_topreal1~np\_\_2~(k1\_sprect\_1~X0))=k11\_pscomp\_1~\\
X0)\end{array}
\label{hyp:ehhdfdpfdhahchfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_sprect\_1~\\
X0)~np\_\_1=k11\_pscomp\_1~X0)\end{array}
\label{hyp:ehddfdpfdhahchfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((v1\_sprect\_1~X0){\unicdbdjded}({\unicdcdaddd} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v2\_compts\_1~\\
X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}((\preoh v1\_sppol\_1~X1){\unicdcdcdhd}((\preoh v2\_sppol\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))))))){\unicdcdcdhd}\\
(X0=k1\_sprect\_1~X1)))\end{array}
\label{hyp:egcdpfdhahchfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidddpfdhahchfgdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_sprect\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~\\
np\_\_1=k20\_pscomp\_1~(k3\_topreal1~np\_\_2~X0)){\unicdcdcdhd}(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1=k19\_pscomp\_1~(k3\_topreal1~np\_\_2~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
