\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{t12\_measure3 (TMTbzGyJSguERqEm82YDwRYsZQKyPenXTK8)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ v10\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_supinf\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_measure1 : {{\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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_supinf\_1 : {\iota}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_measure2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_measure3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_measure1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~k5\_numbers~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
({\unicdcdaddd} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdcdcdhd}\\
((k8\_nat\_1~X1~X3~k6\_numbers=k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k8\_nat\_1~X1~X3~(k2\_nat\_1~X4~np\_\_1)=\\
k3\_measure1~X0~X1~(k8\_nat\_1~X1~X2~k6\_numbers)~(k8\_nat\_1~X1~X2~X4))))))\end{array}
\label{hyp:ehjdpfngfgbgdhfhchfgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~k7\_numbers){\unicdcdcdhd}\\
((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~X2~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
(((k8\_nat\_1~X1~X3~k6\_numbers=k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~\\
X5~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k8\_nat\_1~X1~X3~(k2\_nat\_1~X5~np\_\_1)=\\
k3\_measure1~X0~X1~(k8\_nat\_1~X1~X4~k6\_numbers)~(k8\_nat\_1~X1~X4~X5)){\unicdcdcdhd}\\
(r1\_tarski~(k8\_nat\_1~X1~X4~(k2\_nat\_1~X5~np\_\_1))~(k8\_nat\_1~X1~X4~X5))))){\unicdbdjdcd}\\
((r1\_xxreal\_0~k1\_supinf\_1~(k12\_supinf\_2~X2~(k8\_nat\_1~X1~X4~k6\_numbers))){\unicdcdcdid}\\
(k12\_supinf\_2~X2~(k1\_measure2~X0~X1~(k1\_measure3~X0~X1~X4))=k4\_supinf\_2~\\
(k12\_supinf\_2~X2~(k8\_nat\_1~X1~X4~k6\_numbers))~(k8\_supinf\_2~(k17\_supinf\_2~\\
(k1\_partfun1~k5\_numbers~X1~X1~k7\_numbers~X3~X2)))))))))\end{array}
\label{hyp:ehidpfngfgbgdhfhchfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~k7\_numbers){\unicdcdcdhd}\\
((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~X2~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
(((k8\_nat\_1~X1~X3~k6\_numbers=k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_subset\_1~\\
X5~k1\_numbers~k5\_numbers){\unicdbdjdcd}((k8\_nat\_1~X1~X3~(k2\_nat\_1~X5~np\_\_1)=\\
k3\_measure1~X0~X1~(k8\_nat\_1~X1~X4~k6\_numbers)~(k8\_nat\_1~X1~X4~X5)){\unicdcdcdhd}\\
(r1\_tarski~(k8\_nat\_1~X1~X4~(k2\_nat\_1~X5~np\_\_1))~(k8\_nat\_1~X1~X4~X5))))){\unicdbdjdcd}\\
((r1\_xxreal\_0~k1\_supinf\_1~(k12\_supinf\_2~X2~(k8\_nat\_1~X1~X4~k6\_numbers))){\unicdcdcdid}\\
(k7\_supinf\_2~(k17\_supinf\_2~(k1\_partfun1~k5\_numbers~X1~X1~k7\_numbers~\\
X4~X2))=k4\_supinf\_2~(k12\_supinf\_2~X2~(k8\_nat\_1~X1~X4~k6\_numbers))~\\
(k8\_supinf\_2~(k17\_supinf\_2~(k1\_partfun1~k5\_numbers~X1~X1~k7\_numbers~\\
X3~X2)))))))))\end{array}
\label{hyp:ehbdbdpfngfgbgdhfhchfgdd}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfngfgbgdhfhchfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_prob\_1~X1~X0){\unicdcdcdhd}\\
((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X1~k7\_numbers){\unicdcdcdhd}\\
((v10\_valued\_0~X2){\unicdcdcdhd}((v6\_supinf\_2~X2){\unicdcdcdhd}((v4\_measure1~X2~X0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~k7\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k5\_numbers~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~X1))))){\unicdbdjdcd}\\
(({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}(r1\_tarski~\\
(k8\_nat\_1~X1~X3~(k2\_nat\_1~X4~np\_\_1))~(k8\_nat\_1~X1~X3~X4))){\unicdbdjdcd}((r1\_xxreal\_0~\\
k1\_supinf\_1~(k12\_supinf\_2~X2~(k8\_nat\_1~X1~X3~k6\_numbers))){\unicdcdcdid}(k12\_supinf\_2~\\
X2~(k1\_measure2~X0~X1~(k1\_measure3~X0~X1~X3))=k7\_supinf\_2~(k17\_supinf\_2~\\
(k1\_partfun1~k5\_numbers~X1~X1~k7\_numbers~X3~X2)))))))\end{array}$$
\end{theorem}
\end{document}
