\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{l19\_scmfsa\_i (TMSKx19x6GVYTppT91dK6xFWxLUR2Pd3GUJ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_scmfsa\_i : {\iota}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_scm\_inst : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ k2\_scm\_inst : {\iota}$ be given.
Let $ k1\_scmfsa\_i : {\iota}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_scmfsa\_i){\unicdbdjdcd}(\preoh (\preoh (X0 \in k3\_scm\_inst){\unicdcdcdhd}\\
(\preoh (k2\_compos\_0~k2\_scmfsa\_i~X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~\\
X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k2\_compos\_0~\\
k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}\\
((k2\_compos\_0~k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_5){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~\\
X0{\unicdcdgdad}np\_\_6){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_7){\unicdcdcdhd}(k2\_compos\_0~\\
k2\_scmfsa\_i~X0{\unicdcdgdad}np\_\_8)))))))))){\unicdcdcdhd}((\preoh (X0 \in ReplSep4~(toset~({\uniddcgcg} X1 : \\
\iota .  m2\_subset\_1~X1~k4\_ordinal1~(k7\_card\_1~np\_\_13)))~({\uniddcgcg} X1 : \\
\iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X1 : \\
\iota .  {\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k2\_scm\_inst))~\\
({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~\\
X4~k1\_scmfsa\_i))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \\
\iota .  X1 \in k2\_tarski~np\_\_9~np\_\_10)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  {\uniddcgcg} X4 : \iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~(k11\_finseq\_1~X2~X4~\\
X3))){\unicdcdcdhd}((k2\_compos\_0~k2\_scmfsa\_i~X0=np\_\_9){\unicdcdcdid}(k2\_compos\_0~k2\_scmfsa\_i~\\
X0=np\_\_10))){\unicdcdcdhd}(\preoh (X0 \in ReplSep3~(toset~({\uniddcgcg} X1 : \iota .  m2\_subset\_1~\\
X1~k4\_ordinal1~(k7\_card\_1~np\_\_13)))~({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~k2\_scm\_inst))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  toset~\\
({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k1\_scmfsa\_i))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  X1 \in k2\_tarski~np\_\_11~np\_\_12)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \\
\iota .  {\uniddcgcg} X3 : \iota .  k3\_xtuple\_0~X1~k1\_xboole\_0~(k10\_finseq\_1~X2~X3))){\unicdcdcdhd}\\
((k2\_compos\_0~k2\_scmfsa\_i~X0=np\_\_11){\unicdcdcdid}(k2\_compos\_0~k2\_scmfsa\_i~\\
X0=np\_\_12)))))\end{array}
\label{hyp:ehhdpfdhdgngggdhbgpfjg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_12}}}}\label{hyp:dhahdgbdcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_11}}}}\label{hyp:dhahdgbdbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k5\_xtuple\_0~(k3\_xtuple\_0~X0~\\
X1~X2)=X1\end{array}
\label{hyp:chegfdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdjdpfdhdgngggdhbgpfjg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_scmfsa\_i){\unicdbdjdcd}(((k2\_compos\_0~k2\_scmfsa\_i~\\
X0=np\_\_11){\unicdcdcdid}(k2\_compos\_0~k2\_scmfsa\_i~X0=np\_\_12)){\unicdbdjdcd}(k5\_xtuple\_0~\\
X0=k1\_xboole\_0))\end{array}$$
\end{theorem}
\end{document}
