\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\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{l36\_integra6 (TMPqw8fnrxsLwU2xuSpBC3hgVSKhQU2Ma1z)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k26\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}((X0 \in k1\_xxreal\_1~X1~X2){\unicdbdjded}((r1\_xxreal\_0~X1~X0){\unicdcdcdhd}\\
(r1\_xxreal\_0~X0~X2)))))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}\\
(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}\\
((r1\_integra5~(k3\_integra5~X0~X3)~X4){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~X4~(k3\_integra5~X0~X3))){\unicdcdcdhd}(r1\_tarski~(k3\_integra5~\\
X0~X3)~(k9\_xtuple\_0~X4))))))){\unicdbdjdcd}((r1\_integra5~(k3\_integra5~X1~X2)~\\
X4){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~X4~(k3\_integra5~\\
X1~X2))){\unicdcdcdhd}(r1\_tarski~(k3\_integra5~X1~X2)~(k9\_xtuple\_0~X4)))))))))\end{array}
\label{hyp:ehbdidpfjgogehfghgchbggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k9\_xtuple\_0~X3)){\unicdcdcdhd}((r1\_integra5~\\
(k3\_integra5~X0~X1)~X3){\unicdcdcdhd}(v1\_comseq\_2~(k2\_partfun1~k1\_numbers~\\
k1\_numbers~X3~(k3\_integra5~X0~X1)))))){\unicdbdjdcd}(k4\_integra5~X0~X1~(k26\_valued\_1~\\
k1\_numbers~k1\_numbers~X3~X2)=k4\_real\_1~X2~(k4\_integra5~X0~X1~X3))))))\end{array}
\label{hyp:ehbdadpfjgogehfghgchbggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k1\_rcomp\_1~\\
X0~X1=k1\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X1){\unicdbdjdcd}(k3\_integra5~X0~X1=k1\_rcomp\_1~X0~X1)))\end{array}
\label{hyp:egddpfjgogehfghgchbgfd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgddgdpfjgogehfghgchbggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v1\_xreal\_0~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}\\
((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~X0~X1)~X5){\unicdcdcdhd}((\\
v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~X5~(k3\_integra5~\\
X0~X1))){\unicdcdcdhd}((r1\_tarski~(k3\_integra5~X0~X1)~(k9\_xtuple\_0~X5)){\unicdcdcdhd}((\\
X2 \in k3\_integra5~X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1))))))){\unicdbdjdcd}(k4\_integra5~\\
X2~X3~(k26\_valued\_1~k1\_numbers~k1\_numbers~X5~X4)=k4\_real\_1~X4~(\\
k4\_integra5~X2~X3~X5))))))))\end{array}$$
\end{theorem}
\end{document}
