\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{t43\_integr12 (TMMaRbzmjtBw8BPfLZGw1V7Mv3TrutLDj5J)}
\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 $ v3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_rfunct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_sin\_cos9 : {\iota}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_binop\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_taylor\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_taylor\_1 : {\iota}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_seq\_4 : {{\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}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v3\_rcomp\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}(((r1\_tarski~X0~X5){\unicdcdcdhd}((r2\_relset\_1~\\
k1\_numbers~k1\_numbers~X1~(k3\_rfunct\_1~k1\_numbers~k1\_numbers~(\\
k6\_rfunct\_1~k1\_numbers~k1\_numbers~(k3\_valued\_1~k1\_numbers~k1\_numbers~\\
k1\_numbers~X2~X3))~X4)){\unicdcdcdhd}((r2\_relset\_1~k1\_numbers~k1\_numbers~X4~\\
k2\_sin\_cos9){\unicdcdcdhd}((r1\_tarski~X5~(k2\_rcomp\_1~(k19\_binop\_2~np\_\_1)~\\
np\_\_1)){\unicdcdcdhd}((r2\_relset\_1~k1\_numbers~k1\_numbers~X3~(k1\_taylor\_1~\\
np\_\_2)){\unicdcdcdhd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}((X6 \in X5){\unicdbdjdcd}\\
((k1\_seq\_1~X2~X6=np\_\_1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k1\_seq\_1~X4~X6)~k6\_numbers)))){\unicdcdcdhd}\\
(X5=k1\_relset\_1~k1\_numbers~X1))))))){\unicdbdjdcd}(k2\_integra5~X0~X1=k10\_binop\_2~\\
(k1\_seq\_1~(k32\_valued\_1~k1\_numbers~k1\_numbers~(k1\_partfun1~k1\_numbers~\\
k1\_numbers~k1\_numbers~k1\_numbers~k2\_sin\_cos9~k3\_taylor\_1))~(\\
k4\_seq\_4~X0))~(k1\_seq\_1~(k32\_valued\_1~k1\_numbers~k1\_numbers~(\\
k1\_partfun1~k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~k2\_sin\_cos9~\\
k3\_taylor\_1))~(k5\_seq\_4~X0)))))))))\end{array}
\label{hyp:ehcdpfjgogehfghgchbdcd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfjgogehfghgchbdcd}
$$\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}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v3\_rcomp\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~\\
(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}(((r1\_tarski~X0~X5){\unicdcdcdhd}((r2\_relset\_1~\\
k1\_numbers~k1\_numbers~X1~(k3\_rfunct\_1~k1\_numbers~k1\_numbers~(\\
k6\_rfunct\_1~k1\_numbers~k1\_numbers~(k3\_valued\_1~k1\_numbers~k1\_numbers~\\
k1\_numbers~X2~X3))~X4)){\unicdcdcdhd}((r2\_relset\_1~k1\_numbers~k1\_numbers~X4~\\
k2\_sin\_cos9){\unicdcdcdhd}((r1\_tarski~X5~(k2\_rcomp\_1~(k19\_binop\_2~np\_\_1)~\\
np\_\_1)){\unicdcdcdhd}((r2\_relset\_1~k1\_numbers~k1\_numbers~X3~(k1\_taylor\_1~\\
np\_\_2)){\unicdcdcdhd}(({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}((X6 \in X5){\unicdbdjdcd}\\
((k1\_seq\_1~X1~X6=k12\_binop\_2~np\_\_1~(k11\_binop\_2~(k9\_binop\_2~np\_\_1~\\
(k5\_square\_1~X6))~(k1\_seq\_1~k2\_sin\_cos9~X6))){\unicdcdcdhd}((k1\_seq\_1~X2~X6=\\
np\_\_1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k1\_seq\_1~X4~X6)~k6\_numbers))))){\unicdcdcdhd}(X5=k1\_relset\_1~\\
k1\_numbers~X1))))))){\unicdbdjdcd}(k2\_integra5~X0~X1=k10\_binop\_2~(k1\_seq\_1~\\
(k32\_valued\_1~k1\_numbers~k1\_numbers~(k1\_partfun1~k1\_numbers~\\
k1\_numbers~k1\_numbers~k1\_numbers~k2\_sin\_cos9~k3\_taylor\_1))~(\\
k4\_seq\_4~X0))~(k1\_seq\_1~(k32\_valued\_1~k1\_numbers~k1\_numbers~(\\
k1\_partfun1~k1\_numbers~k1\_numbers~k1\_numbers~k1\_numbers~k2\_sin\_cos9~\\
k3\_taylor\_1))~(k5\_seq\_4~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
