\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{t28\_combgras (TMYzy6nCDbkTCddsxzM7njm3rfJgPSQnbLd)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}((r1\_ordinal1~(k2\_nat\_1~X0~np\_\_1)~(k1\_card\_1~X1)){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdid}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_incsp\_1~\\
(k1\_combgras~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X1)){\unicdbdjdcd}(((k1\_card\_1~X3=k5\_real\_1~X0~np\_\_1){\unicdcdcdhd}(X2=ReplSep~(toset~\\
({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(k1\_zfmisc\_1~X1)))~({\uniddcgcg} X4 : \iota .  (\\
k1\_card\_1~X4=X0){\unicdcdcdhd}(r1\_tarski~X3~X4))~({\uniddcgcg} X4 : \iota .  X4))){\unicdbdjdcd}(X3=k1\_setfam\_1~\\
X2)))))))\end{array}
\label{hyp:ehcdgdpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_incsp\_1~(k1\_combgras~\\
X0~X1)))){\unicdbdjdcd}((v3\_combgras~X2~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~X1)){\unicdcdcdhd}((k1\_card\_1~X3=k5\_real\_1~X0~np\_\_1){\unicdcdcdhd}(X2=ReplSep~\\
(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~(k1\_zfmisc\_1~X1)))~({\uniddcgcg} X4 : \\
\iota .  (k1\_card\_1~X4=X0){\unicdcdcdhd}(r1\_tarski~X3~X4))~({\uniddcgcg} X4 : \iota .  X4)))))))\end{array}
\label{hyp:egedpfdgpgngcghgchbgdh}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfdgpgngcghgchbgdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}((r1\_ordinal1~(k2\_nat\_1~X0~np\_\_1)~(k1\_card\_1~X1)){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdid}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_incsp\_1~\\
(k1\_combgras~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_incsp\_1~(k1\_combgras~X0~X1)))){\unicdbdjdcd}(((v3\_combgras~X2~X0~X1){\unicdcdcdhd}(\\
(v3\_combgras~X3~X0~X1){\unicdcdcdhd}(k1\_setfam\_1~X2=k1\_setfam\_1~X3))){\unicdbdjdcd}(X2=\\
X3)))))))\end{array}$$
\end{theorem}
\end{document}
