\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{l23\_scm\_inst (TMUitvBqL1wkXoi1Nke425hnuvMcD6fqRt6)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_compos\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_scm\_inst : {\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 $ k3\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_compos\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_scm\_inst : {\iota}$ be given.
Let $ k5\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_compos\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{np\_\_1}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehedjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_compos\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~\\
X0){\unicdcdcdhd}(k2\_compos\_0~X0~X2=X1)))\end{array}
\label{hyp:ehbdadpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_scm\_inst}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k1\_tarski~k1\_xboole\_0){\unicdcdcdhd}\\
((k1\_xboole\_0 \in X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_xboole\_0))))\end{array}
\label{hyp:mgedfdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k3\_scm\_inst){\unicdbdjdcd}((\preoh (k2\_compos\_0~k3\_scm\_inst~\\
X0{\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k2\_compos\_0~k3\_scm\_inst~X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k2\_compos\_0~\\
k3\_scm\_inst~X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k2\_compos\_0~k3\_scm\_inst~X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}\\
(k2\_compos\_0~k3\_scm\_inst~X0{\unicdcdgdad}np\_\_5))))){\unicdbdjdcd}(k5\_xtuple\_0~X0=k1\_xboole\_0))\end{array}
\label{hyp:mgbdidpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v2\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdgfdpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k3\_scm\_inst}}}})}{\unicdcdcdhd}{({{v1\_compos\_0}~{k3\_scm\_inst}})}}\label{hyp:ggdgedpfdhdgngpfjgogdheh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_compos\_0~X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k3\_compos\_0~\\
X0~X1)){\unicdcdcdhd}(v4\_funct\_1~(k3\_compos\_0~X0~X1)))\end{array}
\label{hyp:ggdgbdadpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_compos\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_compos\_0~X0)){\unicdbdjdcd}(k3\_compos\_0~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~X0))~({\uniddcgcg} X2 : \iota .  k2\_compos\_0~\\
X0~X2=X1)~({\uniddcgcg} X2 : \iota .  k5\_xtuple\_0~X2)))\end{array}
\label{hyp:egddpfdgpgngahpgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgcdddpfdhdgngpfjgogdheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_compos\_0~k3\_scm\_inst)){\unicdbdjdcd}((\preoh (X0{\unicdcdgdad}\\
np\_\_1){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_2){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_3){\unicdcdcdhd}((X0{\unicdcdgdad}np\_\_4){\unicdcdcdhd}(X0{\unicdcdgdad}np\_\_5))))){\unicdbdjdcd}\\
(k3\_compos\_0~k3\_scm\_inst~X0=k1\_tarski~k1\_xboole\_0))\end{array}$$
\end{theorem}
\end{document}
