\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{t5\_integr15 (TMRvS4cLiJXMvHijkxBh1xLVrTa11LGzjEV)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_measure5 : {{\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\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_integra1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_integra2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_integra1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_integra1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_integra2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_integra1~X2~X0){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_integr15~X3~X0~X1~X2){\unicdbdjdcd}((v2\_seq\_2~(k2\_partfun1~\\
X0~k1\_numbers~X1~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k7\_integra1~X0~X1~X2)~(k1\_integr15~\\
X0~X1~X2~X3))))))\end{array}
\label{hyp:ehbdpfjgogehfghgchbdfd}
\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){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~\\
X0)))))))){\unicdbdjdcd}((v1\_funct\_1~(k4\_integra2~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~\\
(k4\_integra2~X0~X1~X2)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k4\_integra2~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgedpfjgogehfghgchbgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdcdcdhd}\\
(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdcdcdhd}(((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~X0)))))){\unicdcdcdhd}\\
(m2\_integr15~X3~X0~X1~X2)))){\unicdbdjdcd}((v1\_funct\_1~(k3\_integr15~X0~X1~X2~\\
X3)){\unicdcdcdhd}((v1\_funct\_2~(k3\_integr15~X0~X1~X2~X3)~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_integr15~X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgddpfjgogehfghgchbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~\\
X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~X0)))))){\unicdcdcdhd}\\
(m1\_subset\_1~X2~k5\_numbers))){\unicdbdjdcd}(m1\_integra1~(k2\_integra2~X0~X1~\\
X2)~X0)\end{array}
\label{hyp:egehpflgcdpfjgogehfghgchbgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdcdcdhd}\\
(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdcdcdhd}(((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~X0)))))){\unicdcdcdhd}\\
((m2\_integr15~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X4~k5\_numbers))))){\unicdbdjdcd}(m1\_integr15~\\
(k2\_integr15~X0~X1~X2~X3~X4)~X0~X1~(k2\_integra2~X0~X2~X4))\end{array}
\label{hyp:egehpflgcdpfjgogehfghgchbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_integr15~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}((X4=k3\_integr15~\\
X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(k1\_seq\_1~X4~X5=k1\_integr15~X0~X1~(k2\_integra2~X0~X2~X5)~(k2\_integr15~\\
X0~X1~X2~X3~X5))))))))\end{array}
\label{hyp:egedpfjgogehfghgchbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
k1\_numbers))))){\unicdbdjdcd}((X3=k4\_integra2~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k1\_seq\_1~X3~X4=k7\_integra1~X0~X1~(k2\_integra2~\\
X0~X2~X4)))))))\end{array}
\label{hyp:egddpfjgogehfghgchbgcd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfjgogehfghgchbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~k5\_numbers~(k1\_integra1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k1\_integra1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_integr15~X3~X0~X1~X2){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((v2\_seq\_2~(k2\_partfun1~X0~k1\_numbers~\\
X1~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_seq\_1~(k4\_integra2~X0~X1~X2)~X4)~(k1\_seq\_1~\\
(k3\_integr15~X0~X1~X2~X3)~X4)))))))\end{array}$$
\end{theorem}
\end{document}
