\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{t23\_scmpds\_7 (TMRd5r2kEM3evRTZUggegNYguEhQzckXY9A)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_scmpds\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_scmpds\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}(v1\_afinsq\_1~X3))))))){\unicdbdjdcd}\\
((r1\_scmpds\_6~X2~X1~X0){\unicdbdjded}(r1\_scmpds\_6~X2~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
X1)~(k1\_funct\_4~X0~X3))))))\end{array}
\label{hyp:ehcdedpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X3~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v4\_relat\_1~X4~k5\_numbers){\unicdcdcdhd}\\
((v5\_relat\_1~X4~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}\\
((v1\_finset\_1~X4){\unicdcdcdhd}(v1\_afinsq\_1~X4))))))){\unicdbdjdcd}(((k6\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X2=k6\_memstr\_0~np\_\_2~k1\_scmpds\_2~X3){\unicdcdcdhd}((r1\_scmpds\_6~\\
X4~X2~X0){\unicdcdcdhd}(r2\_scmpds\_6~X4~X2~X0))){\unicdbdjdcd}((r1\_scmpds\_6~X4~X3~X1){\unicdcdcdhd}(r2\_scmpds\_6~\\
X4~X3~X1)))))))\end{array}
\label{hyp:ehcdddpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(\preoh v1\_setfam\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}\\
((v3\_extpro\_1~X1~X0){\unicdcdcdhd}(l1\_extpro\_1~X1~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~X2)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_funct\_1~X3~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~X3~(u1\_struct\_0~X1)))))){\unicdbdjdcd}((r1\_extpro\_1~\\
X0~X1~X2~X3){\unicdbdjdcd}(k6\_extpro\_1~X0~X1~X2~X3=k5\_extpro\_1~X0~X1~X2~X3~(k8\_extpro\_1~\\
X0~X1~X2~X3))))))\end{array}
\label{hyp:ehcdddpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~\\
X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}((r1\_scmpds\_6~X2~X1~X0){\unicdbdjded}(r1\_scmpds\_6~X2~(k8\_memstr\_0~\\
np\_\_2~k1\_scmpds\_2~X1)~X0))))\end{array}
\label{hyp:ehbdcdfdpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_2}}}}\label{hyp:dhahdgcdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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)))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~\\
X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k1\_funct\_4~X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k1\_funct\_4~\\
X1~X2)){\unicdcdcdhd}(v1\_partfun1~(k1\_funct\_4~X1~X2)~X0))))\end{array}
\label{hyp:ggdgidpfggfhogdgehpfed}
\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\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}\\
(v1\_funct\_1~X2)))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~\\
(k1\_funct\_4~X1~X2)~X0){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X1~X2))))\end{array}
\label{hyp:ggdghdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}{\unicdcdcdhd}{({{{v3\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}}\label{hyp:ggdgedpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v2\_memstr\_0~k1\_scmpds\_2~np\_\_2){\unicdcdcdhd}((v3\_memstr\_0~k1\_scmpds\_2~np\_\_2){\unicdcdcdhd}\\
(v1\_extpro\_1~k1\_scmpds\_2~np\_\_2))\end{array}
\label{hyp:ggdgcdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k1\_scmpds\_2}}}})}{\unicdcdcdhd}{({{{v1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}}\label{hyp:ggdgbdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_setfam\_1~X0){\unicdcdcdhd}(((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v2\_memstr\_0~X1~X0){\unicdcdcdhd}((v3\_memstr\_0~X1~X0){\unicdcdcdhd}(l1\_memstr\_0~X1~\\
X0)))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}(\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~X0~X1)){\unicdcdcdhd}(v1\_partfun1~\\
X2~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}((v1\_relat\_1~(k8\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k8\_memstr\_0~X0~X1~X2)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k8\_memstr\_0~X0~X1~X2)){\unicdcdcdhd}((v5\_funct\_1~(k8\_memstr\_0~X0~X1~X2)~(k2\_memstr\_0~\\
X0~X1)){\unicdcdcdhd}(v1\_partfun1~(k8\_memstr\_0~X0~X1~X2)~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:ggdgbdedpfngfgngdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_compos\_1~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}\\
((\preoh v1\_xboole\_0~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}((v1\_relat\_1~(k10\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_compos\_1~X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
(k10\_compos\_1~X0~X1)~(u1\_compos\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k10\_compos\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_finset\_1~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}(v1\_afinsq\_1~(k10\_compos\_1~\\
X0~X1))))))))\end{array}
\label{hyp:ggdgbdddpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}\\
(v1\_funct\_1~X2)))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X1~X2)){\unicdcdcdhd}((v5\_relat\_1~\\
(k1\_funct\_4~X1~X2)~X0){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X1~X2))))\end{array}
\label{hyp:ggdgbdadpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_extpro\_1~X1~X0){\unicdbdjdcd}((l1\_memstr\_0~X1~X0){\unicdcdcdhd}\\
(l1\_compos\_1~X1))\end{array}
\label{hyp:egehpfmgbdpffgihehahchpgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~\\
X0))))))){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~k5\_numbers))))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k6\_scmpds\_4~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k6\_scmpds\_4~\\
X0~X1~X2)~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~(k6\_scmpds\_4~\\
X0~X1~X2)){\unicdcdcdhd}((v5\_funct\_1~(k6\_scmpds\_4~X0~X1~X2)~(k2\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2)){\unicdcdcdhd}(v1\_partfun1~(k6\_scmpds\_4~X0~X1~X2)~(u1\_struct\_0~\\
k1\_scmpds\_2))))))\end{array}
\label{hyp:egehpflggdpfdhdgngahegdhpfed}
\end{equation}
Assume the following.
\begin{equation}
{{({{{v1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}{\unicdcdcdhd}{({{{l1\_extpro\_1}~{k1\_scmpds\_2}}~{np\_\_2}})}}\label{hyp:egehpflgbdpfdhdgngahegdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_4~X0~\\
X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_4~X0~X1)))\end{array}
\label{hyp:egehpflgbdpfggfhogdgehpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l1\_compos\_1~X0){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~(u1\_compos\_1~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_afinsq\_1~X1))))))){\unicdbdjdcd}\\
((v1\_relat\_1~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}((v4\_relat\_1~(k10\_compos\_1~\\
X0~X1)~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~(k10\_compos\_1~X0~X1)~(u1\_compos\_1~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k10\_compos\_1~X0~X1)){\unicdcdcdhd}(v1\_finset\_1~(k10\_compos\_1~\\
X0~X1))))))\end{array}
\label{hyp:egehpflgbdadpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~\\
(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~\\
k5\_numbers))))){\unicdbdjdcd}(k6\_scmpds\_4~X0~X1~X2=k6\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
(k1\_funct\_4~X2~(k10\_compos\_1~k1\_scmpds\_2~X0))~X1)))\end{array}
\label{hyp:egfdpfdhdgngahegdhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_funct\_1~X1~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X1~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~\\
(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~\\
k5\_numbers))))){\unicdbdjdcd}((r2\_scmpds\_6~X0~X1~X2){\unicdbdjded}(r1\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
(k1\_funct\_4~X2~(k10\_compos\_1~k1\_scmpds\_2~X0))~(k8\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X1)))))\end{array}
\label{hyp:egddpfdhdgngahegdhpfgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v1\_finset\_1}~{X0}})}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v7\_ordinal1~X0){\unicdcdcdhd}(\preoh v1\_setfam\_1~X0)))\end{array}
\label{hyp:dgdgbdpfbgngjgpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfdhdgngahegdhpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_2~k1\_scmpds\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmpds\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X1~\\
(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~\\
k5\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X2~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}(v1\_afinsq\_1~\\
X2))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v4\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~X3~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_finset\_1~X3){\unicdcdcdhd}(v1\_afinsq\_1~X3))))))){\unicdbdjdcd}\\
(((r2\_scmpds\_6~X2~X0~X1){\unicdcdcdhd}((r1\_scmpds\_6~X3~(k6\_scmpds\_4~X2~(k8\_memstr\_0~\\
np\_\_2~k1\_scmpds\_2~X0)~X1)~X1){\unicdcdcdhd}(r2\_scmpds\_6~X3~(k6\_scmpds\_4~X2~(\\
k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0)~X1)~X1))){\unicdbdjdcd}((r1\_scmpds\_6~X3~(\\
k5\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k1\_funct\_4~X1~(k10\_compos\_1~k1\_scmpds\_2~\\
X2))~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0)~(k8\_extpro\_1~np\_\_2~k1\_scmpds\_2~\\
(k1\_funct\_4~X1~(k10\_compos\_1~k1\_scmpds\_2~X2))~(k8\_memstr\_0~np\_\_2~\\
k1\_scmpds\_2~X0)))~(k1\_funct\_4~X1~(k10\_compos\_1~k1\_scmpds\_2~X2))){\unicdcdcdhd}\\
(r2\_scmpds\_6~X3~(k5\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k1\_funct\_4~X1~\\
(k10\_compos\_1~k1\_scmpds\_2~X2))~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~\\
X0)~(k8\_extpro\_1~np\_\_2~k1\_scmpds\_2~(k1\_funct\_4~X1~(k10\_compos\_1~\\
k1\_scmpds\_2~X2))~(k8\_memstr\_0~np\_\_2~k1\_scmpds\_2~X0)))~(k1\_funct\_4~\\
X1~(k10\_compos\_1~k1\_scmpds\_2~X2))))))))\end{array}$$
\end{theorem}
\end{document}
