\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{t19\_msualg\_8 (TMG4tr8k7Vq781rHCUfsfXCfp9EbtsJ7Mtt)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_msualg\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_msualg\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_msualg\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k16\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_nat\_lat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k6\_msualg\_5~\\
X0~X1)))){\unicdbdjdcd}((v2\_msualg\_4~(k16\_lattice3~(k5\_msualg\_5~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1))~X2)~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~(k16\_lattice3~\\
(k5\_msualg\_5~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1))~X2)~X0~X1){\unicdcdcdhd}(\\
m1\_msualg\_4~(k16\_lattice3~(k5\_msualg\_5~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~X1))~X2)~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~\\
X1))))))\end{array}
\label{hyp:ehbdbdpfngdhfhbgmghgpfid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_struct\_0~X0){\unicdcdcdhd}(l2\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
((v1\_relat\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(u3\_msualg\_1~\\
X0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~(u3\_msualg\_1~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
(u3\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:egehpffhddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l3\_msualg\_1~X1~X0){\unicdbdjdcd}(l2\_msualg\_1~X1~X0))\end{array}
\label{hyp:egehpfmgddpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((v3\_lattices~(k6\_msualg\_5~X0~X1)){\unicdcdcdhd}(m2\_nat\_lat~(k6\_msualg\_5~\\
X0~X1)~(k5\_msualg\_5~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1))))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0))))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k5\_msualg\_5~X0~X1)){\unicdcdcdhd}((v3\_lattices~(k5\_msualg\_5~\\
X0~X1)){\unicdcdcdhd}((v10\_lattices~(k5\_msualg\_5~X0~X1)){\unicdcdcdhd}(l3\_lattices~(k5\_msualg\_5~\\
X0~X1)))))\end{array}
\label{hyp:egehpflgfdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v3\_lattices~X2){\unicdcdcdhd}(m2\_nat\_lat~X2~(k5\_msualg\_5~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)))){\unicdbdjdcd}((X2=k6\_msualg\_5~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in u1\_struct\_0~X2){\unicdbdjded}((v2\_msualg\_4~X3~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X3~\\
X0~X1){\unicdcdcdhd}(m1\_msualg\_4~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~\\
X0~X1))))))))\end{array}
\label{hyp:eggdpfngdhfhbgmghgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_nat\_lat~X1~X0){\unicdbdjdcd}((v1\_msualg\_7~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X1))){\unicdbdjdcd}(k16\_lattice3~\\
X0~X2 \in u1\_struct\_0~X1))))\end{array}
\label{hyp:egcdpfngdhfhbgmghgpfhd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfngdhfhbgmghgpfid}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}\\
(v1\_msualg\_7~(k6\_msualg\_5~X0~X1)~(k5\_msualg\_5~(u1\_struct\_0~X0)~\\
(u3\_msualg\_1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
