\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\_osalg\_4 (TMakLXEik9Ekr7Ptvwy1CoZcBw8zSnHt64h)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_osalg\_4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v12\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_osalg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r6\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k16\_osalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k19\_osalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r4\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k21\_osalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r5\_msualg\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_msualg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_osalg\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}((v12\_osalg\_1~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}(((r2\_msualg\_3~X0~\\
X1~X2~X3){\unicdcdcdhd}(v1\_osalg\_3~X3~X0)){\unicdbdjdcd}(r4\_msualg\_3~X0~(k16\_osalg\_4~X0~X1~\\
(k19\_osalg\_4~X0~X1~X2~X3))~X2~(k21\_osalg\_4~X0~X1~X2~X3))))))\end{array}
\label{hyp:ehbdidpfpgdhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}((l3\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~\\
X0))){\unicdbdjdcd}((r6\_msualg\_3~X0~X1~X2){\unicdbdjded}(r5\_msualg\_3~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchgdpfngdhfhbgmghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_osalg\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_osalg\_1}~{X0}})}})}}}\label{hyp:egehpfmgddpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_msualg\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}\\
((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}\\
((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}(((v4\_msualg\_1~X2~\\
X0){\unicdcdcdhd}((v12\_osalg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0))){\unicdcdcdhd}(m2\_pboole~X3~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2))))){\unicdbdjdcd}(\\
m2\_pboole~(k21\_osalg\_4~X0~X1~X2~X3)~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~(k16\_osalg\_4~X0~X1~(k19\_osalg\_4~X0~X1~X2~X3)))~(u3\_msualg\_1~X0~\\
X2))\end{array}
\label{hyp:egehpflgcdbdpfpgdhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}\\
((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}\\
((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}(((v4\_msualg\_1~X2~\\
X0){\unicdcdcdhd}((v12\_osalg\_1~X2~X0){\unicdcdcdhd}(l3\_msualg\_1~X2~X0))){\unicdcdcdhd}(m2\_pboole~X3~\\
(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2))))){\unicdbdjdcd}(\\
(v2\_msualg\_4~(k19\_osalg\_4~X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~(k19\_osalg\_4~\\
X0~X1~X2~X3)~X0~X1){\unicdcdcdhd}(m1\_osalg\_4~(k19\_osalg\_4~X0~X1~X2~X3)~X0~X1)))\end{array}
\label{hyp:egehpflgbdjdpfpgdhbgmghgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~\\
X0)))))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdcdcdhd}((v2\_msualg\_4~X2~X0~X1){\unicdcdcdhd}((v3\_msualg\_4~X2~X0~X1){\unicdcdcdhd}(m1\_osalg\_4~\\
X2~X0~X1))))){\unicdbdjdcd}((v12\_osalg\_1~(k16\_osalg\_4~X0~X1~X2)~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
(k16\_osalg\_4~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflgbdgdpfpgdhbgmghgpfed}
\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 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (l3\_msualg\_1~\\
X2~X0){\unicdbdjdcd}((r5\_msualg\_3~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_pboole~X3~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdcdcdhd}(r4\_msualg\_3~X0~X1~\\
X2~X3)))))\end{array}
\label{hyp:egbdbdpfngdhfhbgmghgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfpgdhbgmghgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}((v2\_osalg\_4~X0){\unicdcdcdhd}(l3\_osalg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_msualg\_1~X2~X0){\unicdcdcdhd}((v12\_osalg\_1~X2~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_pboole~X3~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)~(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}(((r2\_msualg\_3~X0~\\
X1~X2~X3){\unicdcdcdhd}(v1\_osalg\_3~X3~X0)){\unicdbdjdcd}(r6\_msualg\_3~X0~(k16\_osalg\_4~X0~X1~\\
(k19\_osalg\_4~X0~X1~X2~X3))~X2)))))\end{array}$$
\end{theorem}
\end{document}
