\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{t25\_scmfsa8c (TMPB4qfaT9JUutcRLsMJaKgqn4NJ2rJXLrE)}
\maketitle
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa8b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_scmfsa8b : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k2\_afinsq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}(\\
(k6\_numbers \in k9\_xtuple\_0~(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((np\_\_1 \in k9\_xtuple\_0~\\
(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((k6\_numbers \in k9\_xtuple\_0~(k2\_scmfsa8b~\\
X0~X1~X2)){\unicdcdcdhd}(np\_\_1 \in k9\_xtuple\_0~(k2\_scmfsa8b~X0~X1~X2)))))))\end{array}
\label{hyp:mgbdfdpfdhdgngggdhbgidcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~\\
X1))))))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k2\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((v1\_relat\_1~(k2\_scmfsa8b~\\
X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k2\_scmfsa8b~X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k2\_scmfsa8b~X0~X1~X2)~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~\\
(k2\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k2\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}\\
(v1\_afinsq\_1~(k2\_scmfsa8b~X0~X1~X2))))))))\end{array}
\label{hyp:egehpflgcdpfdhdgngggdhbgidcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdcdcdhd}(((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~\\
X1))))))){\unicdcdcdhd}((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((v1\_relat\_1~(k1\_scmfsa8b~\\
X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k1\_scmfsa8b~X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k1\_scmfsa8b~X0~X1~X2)~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~\\
(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}\\
(v1\_afinsq\_1~(k1\_scmfsa8b~X0~X1~X2))))))))\end{array}
\label{hyp:egehpflgbdpfdhdgngggdhbgidcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)))\end{array}
\label{hyp:dgdgjdpfbgggjgogdhbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfdhdgngggdhbgiddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~\\
X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~k1\_scmfsa\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~X2))))))){\unicdbdjdcd}(\\
(k6\_numbers \in k2\_afinsq\_1~(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((np\_\_1 \in k2\_afinsq\_1~\\
(k1\_scmfsa8b~X0~X1~X2)){\unicdcdcdhd}((k6\_numbers \in k2\_afinsq\_1~(k2\_scmfsa8b~\\
X0~X1~X2)){\unicdcdcdhd}(np\_\_1 \in k2\_afinsq\_1~(k2\_scmfsa8b~X0~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
