\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{t16\_integr16 (TMGSkK92wV9YNved4HFKSV2ztMVt9DANsTV)}
\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_integr16 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_integr16 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_comseq\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_comseq\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_comseq\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_integra1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((r2\_relset\_1~X0~X1~X2~X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k2\_numbers)))){\unicdbdjdcd}(k6\_comseq\_3~X0~X1=k4\_comseq\_3~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k2\_numbers)))){\unicdbdjdcd}(k5\_comseq\_3~X0~X1=k3\_comseq\_3~\\
X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}(k1\_integra5~X0~\\
X1=k5\_relat\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfjgogehfghgchbgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k2\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k1\_numbers)){\unicdbdjdcd}((r2\_relset\_1~k1\_numbers~k1\_numbers~(k5\_comseq\_3~\\
k1\_numbers~(k2\_partfun1~k1\_numbers~k2\_numbers~X0~X1))~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~(k5\_comseq\_3~k1\_numbers~X0)~X1)){\unicdcdcdhd}(r2\_relset\_1~\\
k1\_numbers~k1\_numbers~(k6\_comseq\_3~k1\_numbers~(k2\_partfun1~k1\_numbers~\\
k2\_numbers~X0~X1))~(k2\_partfun1~k1\_numbers~k1\_numbers~(k6\_comseq\_3~\\
k1\_numbers~X0)~X1))))\end{array}
\label{hyp:mgcdhdpfjgogehfghgchbdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k2\_numbers)))){\unicdbdjdcd}((v1\_funct\_1~(k6\_comseq\_3~X0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(k6\_comseq\_3~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))\end{array}
\label{hyp:egehpflggdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k2\_numbers)))){\unicdbdjdcd}((v1\_funct\_1~(k5\_comseq\_3~X0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(k5\_comseq\_3~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k1\_numbers))))\end{array}
\label{hyp:egehpflgfdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_partfun1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~X0~X1~X2~X3)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogbd}
\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~k1\_numbers~k2\_numbers)))){\unicdbdjdcd}\\
((r1\_integr16~X0~X1){\unicdbdjded}((r1\_integra5~X0~(k5\_comseq\_3~k1\_numbers~\\
X1)){\unicdcdcdhd}(r1\_integra5~X0~(k6\_comseq\_3~k1\_numbers~X1)))))\end{array}
\label{hyp:eghdpfjgogehfghgchbdgd}
\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~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~X0~k2\_numbers))))){\unicdbdjdcd}((v1\_integr16~X1~X0){\unicdbdjded}((v3\_integra1~\\
(k5\_comseq\_3~X0~X1)~X0){\unicdcdcdhd}(v3\_integra1~(k6\_comseq\_3~X0~X1)~X0))))\end{array}
\label{hyp:egfdpfjgogehfghgchbdgd}
\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~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
((r1\_integra5~X0~X1){\unicdbdjded}(v3\_integra1~(k1\_integra5~X1~X0)~X0)))\end{array}
\label{hyp:egbdpfjgogehfghgchbgfd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfjgogehfghgchbdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v2\_measure5~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k2\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k2\_numbers))))){\unicdbdjdcd}\\
((k2\_partfun1~k1\_numbers~k2\_numbers~X1~X0=X2){\unicdbdjdcd}((r1\_integr16~\\
X0~X1){\unicdbdjded}(v1\_integr16~X2~X0)))))\end{array}$$
\end{theorem}
\end{document}
