\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{t39\_osalg\_2 (TMJkhJcL5FhJCLsSvWEcuJecXKpFVq8RVBJ)}
\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 $ 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 $ m1\_msualg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k11\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r8\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~\\
X1~X0){\unicdbdjdcd}((v12\_osalg\_1~X1~X0){\unicdbdjded}((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)){\unicdcdcdhd}(v11\_osalg\_1~(u3\_msualg\_1~X0~X1)~X0)))))))\end{array}
\label{hyp:ehbdhdpfpgdhbgmghgpfbd}
\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}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_msualg\_2~\\
X2~X0~X1){\unicdbdjdcd}(l3\_msualg\_1~X2~X0))\end{array}
\label{hyp:egehpfngbdpfngdhfhbgmghgpfcd}
\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}\\
(l3\_osalg\_1~X0))))){\unicdcdcdhd}(((v4\_msualg\_1~X1~X0){\unicdcdcdhd}((v12\_osalg\_1~X1~X0){\unicdcdcdhd}\\
(l3\_msualg\_1~X1~X0))){\unicdcdcdhd}(((v12\_osalg\_1~X2~X0){\unicdcdcdhd}(m1\_msualg\_2~X2~X0~\\
X1)){\unicdcdcdhd}((v12\_osalg\_1~X3~X0){\unicdcdcdhd}(m1\_msualg\_2~X3~X0~X1))))){\unicdbdjdcd}((v3\_msualg\_1~\\
(k11\_osalg\_2~X0~X1~X2~X3)~X0){\unicdcdcdhd}((v12\_osalg\_1~(k11\_osalg\_2~X0~X1~X2~\\
X3)~X0){\unicdcdcdhd}(m1\_msualg\_2~(k11\_osalg\_2~X0~X1~X2~X3)~X0~X1)))\end{array}
\label{hyp:egehpflgbdbdpfpgdhbgmghgpfcd}
\end{equation}
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}(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 .  \\
((v12\_osalg\_1~X2~X0){\unicdcdcdhd}(m1\_msualg\_2~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v12\_osalg\_1~\\
X3~X0){\unicdcdcdhd}(m1\_msualg\_2~X3~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v3\_msualg\_1~X4~X0){\unicdcdcdhd}\\
((v12\_osalg\_1~X4~X0){\unicdcdcdhd}(m1\_msualg\_2~X4~X0~X1))){\unicdbdjdcd}((X4=k11\_osalg\_2~\\
X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (m2\_osalg\_2~X5~X0~X1){\unicdbdjdcd}((r8\_pboole~(u1\_struct\_0~\\
X0)~X5~(k2\_pboole~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X2)~(u3\_msualg\_1~\\
X0~X3))){\unicdbdjdcd}(X4=k10\_osalg\_2~X0~X1~X5))))))))\end{array}
\label{hyp:egbdddpfpgdhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
(k2\_pboole~X0~X1~X2=k2\_pboole~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfahcgpgpgmgfg}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfpgdhbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_msualg\_1~\\
X1~X0){\unicdcdcdhd}((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v12\_osalg\_1~X2~X0){\unicdcdcdhd}(m1\_msualg\_2~X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v12\_osalg\_1~\\
X3~X0){\unicdcdcdhd}(m1\_msualg\_2~X3~X0~X1)){\unicdbdjdcd}(k11\_osalg\_2~X0~X1~X2~X3=k11\_osalg\_2~\\
X0~X1~X3~X2))))\end{array}$$
\end{theorem}
\end{document}
