\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}
\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{t23\_integr19 (TMKMhtxc3ag5F5xWmAW2VTV2uMPtdp3ZapT)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ 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\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nfcont\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_integr15 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_integr15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_integra5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
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 .  ((\preoh \\
v1\_xboole\_0~X4){\unicdcdcdhd}(m2\_subset\_1~X4~k1\_numbers~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
(k1\_euclid~X4))))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}\\
((r1\_integr15~X4~(k3\_integra5~X0~X1)~X5){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~(k1\_nfcont\_4~X4~k1\_numbers~X5)){\unicdcdcdhd}((v3\_integr15~(k2\_partfun1~\\
k1\_numbers~(k1\_euclid~X4)~X5~(k3\_integra5~X0~X1))~X4){\unicdcdcdhd}((r1\_tarski~\\
(k3\_integra5~X0~X1)~(k1\_relset\_1~k1\_numbers~X5)){\unicdcdcdhd}((X2 \in k3\_integra5~\\
X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1)))))))){\unicdbdjdcd}(r1\_xxreal\_0~(k12\_euclid~\\
(k12\_integr15~X3~X2~X4~X5))~(k4\_integra5~X2~X3~(k1\_nfcont\_4~X4~k1\_numbers~\\
X5)))))))))\end{array}
\label{hyp:mgddedpfjgogehfghgchbdjd}
\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 .  ((\preoh \\
v1\_xboole\_0~X4){\unicdcdcdhd}(m2\_subset\_1~X4~k1\_numbers~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
(k1\_euclid~X4))))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}\\
((r1\_integr15~X4~(k3\_integra5~X0~X1)~X5){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~(k1\_nfcont\_4~X4~k1\_numbers~X5)){\unicdcdcdhd}((v3\_integr15~(k2\_partfun1~\\
k1\_numbers~(k1\_euclid~X4)~X5~(k3\_integra5~X0~X1))~X4){\unicdcdcdhd}((r1\_tarski~\\
(k3\_integra5~X0~X1)~(k1\_relset\_1~k1\_numbers~X5)){\unicdcdcdhd}((X2 \in k3\_integra5~\\
X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1)))))))){\unicdbdjdcd}((r1\_integr15~X4~(k3\_integra5~\\
X2~X3)~X5){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~X2~X3)~(k1\_nfcont\_4~X4~k1\_numbers~\\
X5)){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~k1\_numbers~k1\_numbers~(k1\_nfcont\_4~\\
X4~k1\_numbers~X5)~(k3\_integra5~X2~X3))){\unicdcdcdhd}(r1\_xxreal\_0~(k12\_euclid~\\
(k12\_integr15~X2~X3~X4~X5))~(k4\_integra5~X2~X3~(k1\_nfcont\_4~X4~k1\_numbers~\\
X5))))))))))))\end{array}
\label{hyp:mgddbdpfjgogehfghgchbdjd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfjgogehfghgchbdjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xreal\_0~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  ((\preoh \\
v1\_xboole\_0~X4){\unicdcdcdhd}(m2\_subset\_1~X4~k1\_numbers~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~\\
(k1\_euclid~X4))))){\unicdbdjdcd}(((r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((r1\_xxreal\_0~X2~X3){\unicdcdcdhd}\\
((r1\_integr15~X4~(k3\_integra5~X0~X1)~X5){\unicdcdcdhd}((r1\_integra5~(k3\_integra5~\\
X0~X1)~(k1\_nfcont\_4~X4~k1\_numbers~X5)){\unicdcdcdhd}((v3\_integr15~(k2\_partfun1~\\
k1\_numbers~(k1\_euclid~X4)~X5~(k3\_integra5~X0~X1))~X4){\unicdcdcdhd}((r1\_tarski~\\
(k3\_integra5~X0~X1)~(k1\_relset\_1~k1\_numbers~X5)){\unicdcdcdhd}((X2 \in k3\_integra5~\\
X0~X1){\unicdcdcdhd}(X3 \in k3\_integra5~X0~X1)))))))){\unicdbdjdcd}((r1\_integra5~(k3\_integra5~\\
X2~X3)~(k1\_nfcont\_4~X4~k1\_numbers~X5)){\unicdcdcdhd}((v1\_comseq\_2~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~(k1\_nfcont\_4~X4~k1\_numbers~X5)~(k3\_integra5~\\
X2~X3))){\unicdcdcdhd}((r1\_xxreal\_0~(k12\_euclid~(k12\_integr15~X2~X3~X4~X5))~\\
(k4\_integra5~X2~X3~(k1\_nfcont\_4~X4~k1\_numbers~X5))){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k12\_euclid~(k12\_integr15~X3~X2~X4~X5))~(k4\_integra5~X2~X3~(k1\_nfcont\_4~\\
X4~k1\_numbers~X5))))))))))))\end{array}$$
\end{theorem}
\end{document}
