\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{t19\_pdiff\_7 (TMWpctpXvDx8SV75jWjSqetxZGANHNy4jvx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}((k8\_euclid~X0~\\
(k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X1~X2)~X3)~\\
X2=k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X1~(k5\_euclid~\\
X0))~(k10\_binop\_2~X3~(k1\_seq\_1~(k1\_pdiff\_1~X1~X0)~X2))){\unicdcdcdhd}(k8\_euclid~\\
X0~X2~(k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X1~X2)~\\
X3)=k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X1~(k5\_euclid~\\
X0))~(k10\_binop\_2~(k1\_seq\_1~(k1\_pdiff\_1~X1~X0)~X2)~X3))))))\end{array}
\label{hyp:ehgdpfahegjgggggpfhd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfahegjgggggpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k1\_numbers~(k1\_euclid~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X4){\unicdcdcdhd}((r1\_xxreal\_0~X4~X0){\unicdcdcdhd}(X2=k1\_seq\_1~(k1\_pdiff\_1~X4~X0)~\\
X3))){\unicdbdjdcd}((k8\_euclid~X0~(k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~\\
X0~X4~X3)~X1)~X3=k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~\\
X0~X4~(k5\_euclid~X0))~(k10\_binop\_2~X1~X2)){\unicdcdcdhd}(k8\_euclid~X0~X3~(k3\_funct\_2~\\
k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X4~X3)~X1)=k3\_funct\_2~\\
k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~X4~(k5\_euclid~X0))~(k10\_binop\_2~\\
X2~X1))))))))\end{array}$$
\end{theorem}
\end{document}
