\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{t26\_osalg\_2 (TMKtTMPdLqEPJcPavforWTwGRJ1b2MEMffc)}
\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 $ v12\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_struct\_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 $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_msualg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v11\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{r1\_tarski}~{({{k1\_setfam\_1}~{X1}})}}~{X0}})}}}}\label{hyp:ehddpfdhfgehggbgngpfbd}
\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 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l3\_msualg\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m3\_pboole~X3~(u1\_struct\_0~X0)~\\
(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m3\_pboole~X4~(u1\_struct\_0~X0)~\\
(u3\_msualg\_1~X0~X2)){\unicdbdjdcd}((r2\_pboole~(u1\_struct\_0~X0)~X3~X4){\unicdbdjdcd}(r1\_tarski~\\
(k1\_funct\_1~(k3\_relat\_1~(u1\_msualg\_1~X0)~(k6\_finseq\_2~(u1\_struct\_0~\\
X0)~X3))~X1)~(k1\_funct\_1~(k3\_relat\_1~(u1\_msualg\_1~X0)~(k6\_finseq\_2~\\
(u1\_struct\_0~X0)~X4))~X1)))))))\end{array}
\label{hyp:ehcdpfngdhfhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pboole~\\
X2~X0~X1){\unicdbdjdcd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}\\
(v1\_partfun1~X2~X0)))))\end{array}
\label{hyp:egehpfngddpfahcgpgpgmgfg}
\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}\\
((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdcdcdhd}((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
(m3\_pboole~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)))\end{array}
\label{hyp:egehpfngcdpfpgdhbgmghgpfcd}
\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}
\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 .  {{({{l2\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_msualg\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_orders\_2}~{X0}})}})}}}\label{hyp:egehpfmgcdpfpgdhbgmghgpfbd}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\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}(l3\_osalg\_1~X0))))){\unicdcdcdhd}\\
(((v12\_osalg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdcdcdhd}(m2\_osalg\_2~X2~X0~X1))){\unicdbdjdcd}\\
(m2\_osalg\_2~(k9\_osalg\_2~X0~X1~X2)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfpgdhbgmghgpfcd}
\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 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
(k5\_osalg\_2~X0~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~\\
(k5\_msualg\_2~X0~X1~X2)))~({\uniddcgcg} X3 : \iota .  (v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_partfun1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(v11\_osalg\_1~X3~X0)))))~({\uniddcgcg} X3 : \iota .  X3))))\end{array}
\label{hyp:eghdpfpgdhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
((r2\_pboole~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}(r1\_tarski~(k1\_funct\_1~\\
X1~X3)~(k1\_funct\_1~X2~X3)))))\end{array}
\label{hyp:egcdpfahcgpgpgmgfg}
\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 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_osalg\_2~X3~X0~X1){\unicdbdjdcd}((X3=k9\_osalg\_2~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k1\_setfam\_1~\\
(k8\_osalg\_2~X0~X1~X2~X4)))))))\end{array}
\label{hyp:egbdbdpfpgdhbgmghgpfcd}
\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 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (X4=\\
k8\_osalg\_2~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (X5 \in X4){\unicdbdjded}({\unicdcdaddd} X6 .  (m2\_osalg\_2~\\
X6~X0~X1){\unicdcdcdhd}((X6 \in k5\_osalg\_2~X0~X1~X2){\unicdcdcdhd}(X5=k1\_funct\_1~X6~X3))))))))\end{array}
\label{hyp:egbdadpfpgdhbgmghgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfpgdhbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_osalg\_2~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_osalg\_2~\\
X4~X0~X1){\unicdbdjdcd}((X4 \in k5\_osalg\_2~X0~X1~X3){\unicdbdjdcd}(r1\_tarski~(k1\_funct\_1~(k3\_relat\_1~\\
(u1\_msualg\_1~X0)~(k6\_finseq\_2~(u1\_struct\_0~X0)~(k9\_osalg\_2~X0~\\
X1~X3)))~X2)~(k1\_funct\_1~(k3\_relat\_1~(u1\_msualg\_1~X0)~(k6\_finseq\_2~\\
(u1\_struct\_0~X0)~X4))~X2)))))))\end{array}$$
\end{theorem}
\end{document}
