\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{t15\_midsp\_2 (TMNfArsqAzFHtzBt9MwY9QH1TuaUJyQnzFg)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_midsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k14\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_midsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_midsp\_1 : {{\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}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(k4\_struct\_0~(k15\_midsp\_1~X0)=k14\_midsp\_1~X0)\end{array}
\label{hyp:ehfdfdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(r1\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~(k15\_midsp\_1~X0))~\\
(u1\_struct\_0~(k15\_midsp\_1~X0)))~(u1\_struct\_0~(k15\_midsp\_1~X0))~\\
(k2\_zfmisc\_1~(k10\_midsp\_1~X0)~(k10\_midsp\_1~X0))~(k10\_midsp\_1~\\
X0)~(u1\_algstr\_0~(k15\_midsp\_1~X0))~(k12\_midsp\_1~X0))\end{array}
\label{hyp:ehfdedpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(u1\_struct\_0~(k15\_midsp\_1~X0)=k10\_midsp\_1~X0)\end{array}
\label{hyp:ehfdddpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_midsp\_1~X1~X0){\unicdbdjded}(X1 \in k10\_midsp\_1~X0))\end{array}
\label{hyp:ehedidpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_0~X0~X1~X2=k5\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_algstr\_0~X0)~X1~X2)))\end{array}
\label{hyp:ehcdpfchmgghfgdgehpfbd}
\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 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(((v1\_funct\_1~X4){\unicdcdcdhd}((\\
v1\_funct\_2~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~X2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X3)))))))){\unicdbdjdcd}((r1\_funct\_2~X0~X1~\\
X2~X3~X4~X5){\unicdbdjded}(X4=X5))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v2\_rlvect\_1~X0){\unicdcdcdhd}(l1\_algstr\_0~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k3\_rlvect\_1~X0~X1~X2=k1\_algstr\_0~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k15\_midsp\_1~X0)){\unicdcdcdhd}(v8\_algstr\_0~(k15\_midsp\_1~\\
X0)))\end{array}
\label{hyp:ggdgedpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k10\_midsp\_1~X0))\end{array}
\label{hyp:ggdgddpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}((v13\_algstr\_0~(k15\_midsp\_1~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k15\_midsp\_1~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k15\_midsp\_1~X0)){\unicdcdcdhd}(v4\_rlvect\_1~(k15\_midsp\_1~\\
X0)))))\end{array}
\label{hyp:ggdgbdpfngjgegdhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_algstr\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_algstr\_0~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~\\
X0){\unicdcdcdhd}(l1\_midsp\_1~X0))){\unicdcdcdhd}((m1\_midsp\_1~X1~X0){\unicdcdcdhd}(m1\_midsp\_1~X2~X0))){\unicdbdjdcd}\\
(m1\_midsp\_1~(k7\_midsp\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflghdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(l2\_algstr\_0~(k15\_midsp\_1~X0))\end{array}
\label{hyp:egehpflgbdfdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(k12\_midsp\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k12\_midsp\_1~\\
X0)~(k2\_zfmisc\_1~(k10\_midsp\_1~X0)~(k10\_midsp\_1~X0))~(k10\_midsp\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k12\_midsp\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k10\_midsp\_1~X0)~(k10\_midsp\_1~X0))~(k10\_midsp\_1~\\
X0))))))\end{array}
\label{hyp:egehpflgbdcdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(k14\_midsp\_1~X0=k6\_midsp\_1~X0)\end{array}
\label{hyp:egbdgdpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
(k10\_midsp\_1~X0)~(k10\_midsp\_1~X0))~(k10\_midsp\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k10\_midsp\_1~X0)~(k10\_midsp\_1~\\
X0))~(k10\_midsp\_1~X0)))))){\unicdbdjdcd}((X1=k12\_midsp\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k10\_midsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k10\_midsp\_1~X0)){\unicdbdjdcd}(k5\_binop\_1~(k10\_midsp\_1~X0)~X1~X2~X3=k11\_midsp\_1~\\
X0~X2~X3)))))\end{array}
\label{hyp:egbdedpfngjgegdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k10\_midsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k10\_midsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k10\_midsp\_1~X0)){\unicdbdjdcd}((X3=k11\_midsp\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_midsp\_1~\\
X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_midsp\_1~X5~X0){\unicdbdjdcd}(((X1=X4){\unicdcdcdhd}(X2=X5)){\unicdbdjdcd}(X3=\\
k7\_midsp\_1~X0~X4~X5))))))))\end{array}
\label{hyp:egbdddpfngjgegdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfngjgegdhahpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_midsp\_1~X0){\unicdcdcdhd}(l1\_midsp\_1~\\
X0))){\unicdbdjdcd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_midsp\_1~\\
X0))){\unicdbdjded}(m1\_midsp\_1~X1~X0)){\unicdcdcdhd}((k4\_struct\_0~(k15\_midsp\_1~X0)=k6\_midsp\_1~\\
X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_midsp\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_midsp\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_midsp\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_midsp\_1~X4~X0){\unicdbdjdcd}\\
(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}(k3\_rlvect\_1~(k15\_midsp\_1~X0)~X1~X2=k7\_midsp\_1~\\
X0~X3~X4))))))))\end{array}$$
\end{theorem}
\end{document}
