\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{l17\_prvect\_2 (TMaLDwAzKpohVq5iHiKF92mxzPhy13bd8UV)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prvect\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k13\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_prvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_prvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_prvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_rlvect\_1 : {{\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 $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdcdcdhd}\\
((m1\_prvect\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k4\_finseq\_1~X0)))){\unicdbdjdcd}(k9\_prvect\_1~\\
X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfahchghfgdgehpfbd}
\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 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\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 v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgidpfchfgmgbgehpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v2\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(k9\_xtuple\_0~\\
X0))){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdgbdbdpfggfhogdgehpfbd}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_rlvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdcdcdhd}\\
((m1\_prvect\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k4\_finseq\_1~X0)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k9\_prvect\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k9\_prvect\_1~X0~X1~X2)~(k2\_zfmisc\_1~\\
(k1\_funct\_1~X0~X2)~(k1\_funct\_1~X0~X2))~(k1\_funct\_1~X0~X2)){\unicdcdcdhd}(m1\_subset\_1~\\
(k9\_prvect\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k1\_funct\_1~X0~X2)~(k1\_funct\_1~X0~X2))~(k1\_funct\_1~X0~X2))))))\end{array}
\label{hyp:egehpflgjdpfahchghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)))){\unicdcdcdhd}((m1\_subset\_1~X1~\\
(k4\_card\_3~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k9\_xtuple\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k8\_prvect\_1~X0~X1~X2)~(k1\_funct\_1~X0~X2))\end{array}
\label{hyp:egehpflgidpfahchghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}(m1\_prvect\_1~(k6\_prvect\_2~\\
X0)~(k4\_prvect\_2~X0))\end{array}
\label{hyp:egehpflggdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k4\_finseq\_1~(k4\_prvect\_2~X0)))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k5\_prvect\_2~\\
X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k5\_prvect\_2~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~(k5\_prvect\_2~\\
X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k5\_prvect\_2~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k5\_prvect\_2~\\
X0~X1)){\unicdcdcdhd}((v5\_rlvect\_1~(k5\_prvect\_2~X0~X1)){\unicdcdcdhd}((v6\_rlvect\_1~(k5\_prvect\_2~\\
X0~X1)){\unicdcdcdhd}((v7\_rlvect\_1~(k5\_prvect\_2~X0~X1)){\unicdcdcdhd}((v8\_rlvect\_1~(k5\_prvect\_2~\\
X0~X1)){\unicdcdcdhd}(l1\_rlvect\_1~(k5\_prvect\_2~X0~X1)))))))))))\end{array}
\label{hyp:egehpflgfdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}((v1\_relat\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((v2\_relat\_1~(k4\_prvect\_2~X0)){\unicdcdcdhd}((v1\_funct\_1~(k4\_prvect\_2~\\
X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k4\_prvect\_2~X0)){\unicdcdcdhd}(v1\_finseq\_1~(k4\_prvect\_2~\\
X0))))))\end{array}
\label{hyp:egehpflgedpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_finseq\_1~X0)~(k1\_zfmisc\_1~k5\_numbers))\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((\\
v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdcdcdhd}(m1\_prvect\_1~\\
X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k13\_prvect\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k13\_prvect\_1~\\
X0~X1)~(k2\_zfmisc\_1~(k4\_card\_3~X0)~(k4\_card\_3~X0))~(k4\_card\_3~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k13\_prvect\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k4\_card\_3~X0)~(k4\_card\_3~X0))~(k4\_card\_3~X0))))))\end{array}
\label{hyp:egehpflgbdddpfahchghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v2\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_prvect\_1~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~\\
(k4\_card\_3~X0)~(k4\_card\_3~X0))~(k4\_card\_3~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_card\_3~X0)~(k4\_card\_3~\\
X0))~(k4\_card\_3~X0)))))){\unicdbdjdcd}((X2=k13\_prvect\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k4\_card\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(\\
k4\_card\_3~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_subset\_1~X5~k5\_numbers~(k4\_finseq\_1~\\
X0)){\unicdbdjdcd}(k8\_prvect\_1~X0~(k12\_prvect\_1~(k4\_card\_3~X0)~X2~X3~X4)~X5=\\
k5\_binop\_1~(k1\_funct\_1~X0~X5)~(k9\_prvect\_1~X0~X1~X5)~(k8\_prvect\_1~\\
X0~X3~X5)~(k8\_prvect\_1~X0~X4~X5))))))))\end{array}
\label{hyp:egidpfahchghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_prvect\_1~\\
X1~(k4\_prvect\_2~X0)){\unicdbdjdcd}((X1=k6\_prvect\_2~X0){\unicdbdjded}((k3\_finseq\_1~X1=\\
k3\_finseq\_1~(k4\_prvect\_2~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k5\_numbers~\\
(k4\_finseq\_1~(k4\_prvect\_2~X0))){\unicdbdjdcd}(r1\_funct\_2~(k2\_zfmisc\_1~(k1\_funct\_1~\\
(k4\_prvect\_2~X0)~X2)~(k1\_funct\_1~(k4\_prvect\_2~X0)~X2))~(k1\_funct\_1~\\
(k4\_prvect\_2~X0)~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~(k5\_prvect\_2~X0~\\
X2))~(u1\_struct\_0~(k5\_prvect\_2~X0~X2)))~(u1\_struct\_0~(k5\_prvect\_2~\\
X0~X2))~(k9\_prvect\_1~(k4\_prvect\_2~X0)~X1~X2)~(u1\_algstr\_0~(k5\_prvect\_2~\\
X0~X2)))))))\end{array}
\label{hyp:egfdpfahchghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (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:egbdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdhdpfahchghfgdgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_finseq\_1~X0){\unicdcdcdhd}(v1\_prvect\_2~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(k4\_card\_3~(k4\_prvect\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~k5\_numbers~\\
(k4\_finseq\_1~(k4\_prvect\_2~X0))){\unicdbdjdcd}((k8\_prvect\_1~(k4\_prvect\_2~\\
X0)~(k12\_prvect\_1~(k4\_card\_3~(k4\_prvect\_2~X0))~(k13\_prvect\_1~\\
(k4\_prvect\_2~X0)~(k6\_prvect\_2~X0))~X1~X2)~X3=k1\_binop\_1~(u1\_algstr\_0~\\
(k5\_prvect\_2~X0~X3))~(k8\_prvect\_1~(k4\_prvect\_2~X0)~X1~X3)~(k8\_prvect\_1~\\
(k4\_prvect\_2~X0)~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k5\_prvect\_2~X0~X3))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
(k5\_prvect\_2~X0~X3))){\unicdbdjdcd}(((X4=k8\_prvect\_1~(k4\_prvect\_2~X0)~X1~X3){\unicdcdcdhd}\\
(X5=k8\_prvect\_1~(k4\_prvect\_2~X0)~X2~X3)){\unicdbdjdcd}(k8\_prvect\_1~(k4\_prvect\_2~\\
X0)~(k12\_prvect\_1~(k4\_card\_3~(k4\_prvect\_2~X0))~(k13\_prvect\_1~\\
(k4\_prvect\_2~X0)~(k6\_prvect\_2~X0))~X1~X2)~X3=k3\_rlvect\_1~(k5\_prvect\_2~\\
X0~X3)~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
