\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{t15\_mesfun7c (TMK6HETdbs3VdFScwVDEhBXecbGgUUQGBVB)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ 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\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_seqfunc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ v10\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mesfunc5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_rinfsup2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_rinfsup2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ v7\_mesfunc5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_seq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_mesfun7c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_mesfunc5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_mesfunc8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
((v10\_mesfunc5~X0){\unicdbdjdcd}((k2\_mesfunc5~X0=k6\_rinfsup2~X0){\unicdcdcdhd}(k2\_mesfunc5~\\
X0=k5\_rinfsup2~X0)))\end{array}
\label{hyp:ehedbdpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k7\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k7\_numbers))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((r1\_funct\_2~k5\_numbers~k7\_numbers~k5\_numbers~k1\_numbers~X0~\\
X1){\unicdcdcdhd}(v2\_comseq\_2~X1)){\unicdbdjdcd}((v7\_mesfunc5~X0){\unicdcdcdhd}((v10\_mesfunc5~X0){\unicdcdcdhd}\\
(k2\_mesfunc5~X0=k2\_seq\_2~X1)))))\end{array}
\label{hyp:ehbdedpfchjgogggdhfhahcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((X2 \in k1\_relset\_1~X0~(k8\_mesfun7c~\\
X0~X1)){\unicdbdjdcd}(k12\_supinf\_2~(k8\_mesfun7c~X0~X1)~X2=k2\_mesfunc5~(k1\_mesfunc5~\\
k5\_numbers~(k10\_seqfunc~X0~X1~X2))))))\end{array}
\label{hyp:ehbdedpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((X2 \in k1\_relset\_1~X0~(k7\_mesfun7c~\\
X0~X1)){\unicdbdjdcd}(k12\_supinf\_2~(k7\_mesfun7c~X0~X1)~X2=k5\_rinfsup2~(k1\_mesfunc5~\\
k5\_numbers~(k10\_seqfunc~X0~X1~X2))))))\end{array}
\label{hyp:ehbdddpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}((X2 \in k1\_relset\_1~X0~(k6\_mesfun7c~\\
X0~X1)){\unicdbdjdcd}(k12\_supinf\_2~(k6\_mesfun7c~X0~X1)~X2=k6\_rinfsup2~(k1\_mesfunc5~\\
k5\_numbers~(k10\_seqfunc~X0~X1~X2))))))\end{array}
\label{hyp:ehbdcdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}(r1\_funct\_2~X0~X1~X2~\\
X3~X4~X4)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k7\_numbers}}}}\label{hyp:ggdgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k8\_mesfun7c~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k8\_mesfun7c~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflgidpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k7\_mesfun7c~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k7\_mesfun7c~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflghdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k6\_mesfun7c~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k6\_mesfun7c~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflggdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k1\_mesfunc5~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_mesfunc5~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k7\_numbers))))\end{array}
\label{hyp:egehpflgbdpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k1\_mesfun7c~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_mesfun7c~\\
X0~X1)~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~(\\
k1\_mesfun7c~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k7\_numbers))))))\end{array}
\label{hyp:egehpflgbdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~\\
X0~k1\_numbers)))))){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}((v1\_funct\_1~(k10\_seqfunc~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k10\_seqfunc~X0~X1~X2)~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~(k10\_seqfunc~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdadpfdhfgbhggfhogdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k7\_numbers)))){\unicdbdjdcd}((X2=k7\_mesfunc8~X0~X1){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~X1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in k1\_relset\_1~X0~X2){\unicdbdjdcd}(k12\_supinf\_2~X2~\\
X3=k2\_mesfunc5~(k3\_mesfunc5~X0~X1~X3))))))))\end{array}
\label{hyp:egjdpfngfgdhggfhogdgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k7\_numbers)))){\unicdbdjdcd}((X2=k6\_mesfunc8~X0~X1){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~X1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in k1\_relset\_1~X0~X2){\unicdbdjdcd}(k12\_supinf\_2~X2~\\
X3=k5\_rinfsup2~(k3\_mesfunc5~X0~X1~X3))))))))\end{array}
\label{hyp:egidpfngfgdhggfhogdgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
(k8\_mesfun7c~X0~X1=k7\_mesfunc8~X0~(k1\_mesfun7c~X0~X1)))\end{array}
\label{hyp:egidpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k7\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~k7\_numbers)))){\unicdbdjdcd}((X2=k5\_mesfunc8~X0~X1){\unicdbdjded}((k1\_relset\_1~X0~X2=\\
k1\_relset\_1~X0~(k4\_mesfunc5~X0~k7\_numbers~X1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}((X3 \in k1\_relset\_1~X0~X2){\unicdbdjdcd}(k12\_supinf\_2~X2~\\
X3=k6\_rinfsup2~(k3\_mesfunc5~X0~X1~X3))))))))\end{array}
\label{hyp:eghdpfngfgdhggfhogdgid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))){\unicdbdjdcd}(\\
k1\_mesfunc5~X0~X1=X1))\end{array}
\label{hyp:eghdpfngfgdhggfhogdgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
(k7\_mesfun7c~X0~X1=k6\_mesfunc8~X0~(k1\_mesfun7c~X0~X1)))\end{array}
\label{hyp:eghdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
(k6\_mesfun7c~X0~X1=k5\_mesfunc8~X0~(k1\_mesfun7c~X0~X1)))\end{array}
\label{hyp:eggdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
(k1\_mesfun7c~X0~X1=X1))\end{array}
\label{hyp:egbdpfngfgdhggfhoghddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v1\_funct\_2~X2~X0~X1){\unicdbdjdcd}(\\
v1\_partfun1~X2~X0)))\end{array}
\label{hyp:dgdgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v1\_partfun1~X2~X0){\unicdbdjdcd}(v1\_funct\_2~X2~X0~X1))\end{array}
\label{hyp:dgdgbdpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfngfgdhggfhoghddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~(k4\_partfun1~X0~k1\_numbers)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(((X2 \in k1\_relset\_1~X0~(k8\_mesfun7c~\\
X0~X1)){\unicdcdcdhd}(v2\_comseq\_2~(k10\_seqfunc~X0~X1~X2))){\unicdbdjdcd}((k12\_supinf\_2~\\
(k8\_mesfun7c~X0~X1)~X2=k12\_supinf\_2~(k7\_mesfun7c~X0~X1)~X2){\unicdcdcdhd}(k12\_supinf\_2~\\
(k8\_mesfun7c~X0~X1)~X2=k12\_supinf\_2~(k6\_mesfun7c~X0~X1)~X2)))))\end{array}$$
\end{theorem}
\end{document}
