\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{t56\_rinfsup1 (TMHv7LKfdsHD5x1Nj1y5o1Rg6ZbkCn9fvMq)}
\maketitle
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 $ 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 $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rinfsup1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_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}((v1\_comseq\_2~\\
X1){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_rinfsup1~(k3\_rinfsup1~X1))~(k1\_seq\_1~(k4\_rinfsup1~\\
X1)~X0))))\end{array}
\label{hyp:ehfdedpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_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}((v1\_comseq\_2~\\
X1){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_seq\_1~(k3\_rinfsup1~X1)~X0)~(k2\_rinfsup1~\\
(k4\_rinfsup1~X1)))))\end{array}
\label{hyp:ehfdddpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_seq\_2~X0){\unicdbdjdcd}(v8\_valued\_0~(k4\_rinfsup1~X0)))\end{array}
\label{hyp:ehfdbdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v2\_seq\_2~X0){\unicdbdjdcd}(v7\_valued\_0~(k3\_rinfsup1~X0)))\end{array}
\label{hyp:ehfdadpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(((v7\_valued\_0~X0){\unicdbdjdcd}(v2\_seq\_2~X0)){\unicdcdcdhd}((v8\_valued\_0~X0){\unicdbdjdcd}(v1\_seq\_2~\\
X0)))\end{array}
\label{hyp:ehbdpfmgjgngggfhogdgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(k1\_seq\_1~X0~X1=k1\_funct\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfgbhpfbd}
\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}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}((r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdid}\\
((\preoh r1\_xxreal\_0~(k2\_xcmplx\_0~X1~X2)~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~X1~(k6\_xcmplx\_0~\\
X0~X2)))))))\end{array}
\label{hyp:mgbdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdghdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~\\
X0))){\unicdbdjdcd}(v1\_xreal\_0~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdggdddpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgfdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_membered}~{k1\_numbers}}\label{hyp:ggdgddpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k4\_rinfsup1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k4\_rinfsup1~X0)~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k4\_rinfsup1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgedpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k3\_rinfsup1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k3\_rinfsup1~X0)~\\
k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k3\_rinfsup1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgddpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k2\_rinfsup1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgcdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_rinfsup1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchjgogggdhfhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v2\_seq\_2~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~(k1\_seq\_1~X0~X2)~X1))))\end{array}
\label{hyp:egedpfdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_seq\_2~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (v1\_xreal\_0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}(\preoh r1\_xxreal\_0~X1~(k1\_seq\_1~X0~X2)))))\end{array}
\label{hyp:egddpfdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v3\_valued\_0~\\
X0){\unicdcdcdhd}((v1\_seq\_2~X0){\unicdcdcdhd}(v2\_seq\_2~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v3\_valued\_0~X0){\unicdcdcdhd}(v1\_comseq\_2~X0))))\end{array}
\label{hyp:dgdgcdpfdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v3\_valued\_0~\\
X0){\unicdcdcdhd}(v1\_comseq\_2~X0)))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((v3\_valued\_0~X0){\unicdcdcdhd}((v1\_seq\_2~X0){\unicdcdcdhd}(v2\_seq\_2~X0)))))\end{array}
\label{hyp:dgdgbdpfdhfgbhpfcd}
\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\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v3\_valued\_0~X2))\end{array}
\label{hyp:dgdgbdidpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehfdgdpfchjgogggdhfhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
((v1\_comseq\_2~X0){\unicdbdjdcd}((v1\_comseq\_2~(k4\_rinfsup1~X0)){\unicdcdcdhd}(v1\_comseq\_2~\\
(k3\_rinfsup1~X0))))\end{array}$$
\end{theorem}
\end{document}
