\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{l15\_scmp\_gcd (TMTfc2w4wVdKrz5xaifwFtFJnd93XfMeuC4)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\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 $ k1\_scmpds\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_scmp\_gcd : {\iota}$ be given.
Let $ k3\_compos\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k5\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_scmp\_gcd : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_scmp\_gcd : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_scmpds\_i : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k3\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k2\_compos\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ k8\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ k16\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k15\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_scmpds\_i : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ k11\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ k4\_scmpds\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\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 $ np\_\_0 : {\iota}$ be given.
Let $ l1\_compos\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{{k5\_card\_1}~{k4\_scmp\_gcd}}={np\_\_15}}\label{hyp:ehidpfdhdgngahpfhgdgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}((X1 \in k2\_afinsq\_1~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~(k5\_card\_1~X0)~X1)))\end{array}
\label{hyp:ehgdgdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjded}((r1\_tarski~\\
(k9\_xtuple\_0~X0)~(k9\_xtuple\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k9\_xtuple\_0~\\
X0){\unicdbdjdcd}(k1\_funct\_1~X0~X2=k1\_funct\_1~X1~X2)))))\end{array}
\label{hyp:ehcdpfhgchggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_funct\_1~k4\_scmp\_gcd~k6\_numbers=k5\_scmpds\_2~k2\_scmp\_gcd~\\
k6\_numbers){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_1=k5\_scmpds\_2~k3\_scmp\_gcd~\\
np\_\_7){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_2=k6\_scmpds\_2~k3\_scmp\_gcd~\\
k15\_scmpds\_i){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_3=k3\_scmpds\_2~np\_\_2){\unicdcdcdhd}\\
((k1\_funct\_1~k4\_scmp\_gcd~np\_\_4=k2\_compos\_1~k1\_scmpds\_2){\unicdcdcdhd}((\\
k1\_funct\_1~k4\_scmp\_gcd~np\_\_5=k8\_scmpds\_2~k3\_scmp\_gcd~np\_\_3~np\_\_9){\unicdcdcdhd}\\
((k1\_funct\_1~k4\_scmp\_gcd~np\_\_6=k16\_scmpds\_2~k3\_scmp\_gcd~k3\_scmp\_gcd~\\
np\_\_6~np\_\_3){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_7=k15\_scmpds\_2~k3\_scmp\_gcd~\\
k3\_scmp\_gcd~np\_\_2~np\_\_3){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_8=k16\_scmpds\_2~\\
k3\_scmp\_gcd~k3\_scmp\_gcd~np\_\_7~np\_\_3){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~\\
np\_\_9=k16\_scmpds\_2~k3\_scmp\_gcd~k2\_scmp\_gcd~(k2\_nat\_1~np\_\_4~k14\_scmpds\_i)~\\
np\_\_1){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_10=k11\_scmpds\_2~k2\_scmp\_gcd~\\
np\_\_1~np\_\_4){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_11=k6\_scmpds\_2~k3\_scmp\_gcd~\\
k15\_scmpds\_i){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_12=k3\_scmpds\_2~\\
(k4\_xcmplx\_0~np\_\_7)){\unicdcdcdhd}((k1\_funct\_1~k4\_scmp\_gcd~np\_\_13=k16\_scmpds\_2~\\
k3\_scmp\_gcd~k3\_scmp\_gcd~np\_\_2~np\_\_6){\unicdcdcdhd}(k1\_funct\_1~k4\_scmp\_gcd~\\
np\_\_14=k4\_scmpds\_2~k3\_scmp\_gcd))))))))))))))\end{array}
\label{hyp:ehbdadpfdhdgngahpfhgdgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_9){\unicdcdcdhd}(m2\_subset\_1~np\_\_9~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_9~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_9~k1\_numbers))\end{array}
\label{hyp:dhahdgjdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_8){\unicdcdcdhd}(m2\_subset\_1~np\_\_8~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_8~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_8~k1\_numbers))\end{array}
\label{hyp:dhahdgidpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_7){\unicdcdcdhd}(m2\_subset\_1~np\_\_7~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_7~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_7~k1\_numbers))\end{array}
\label{hyp:dhahdghdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_6){\unicdcdcdhd}(m2\_subset\_1~np\_\_6~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_6~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_6~k1\_numbers))\end{array}
\label{hyp:dhahdggdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_5){\unicdcdcdhd}(m2\_subset\_1~np\_\_5~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_5~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_5~k1\_numbers))\end{array}
\label{hyp:dhahdgfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_4){\unicdcdcdhd}(m2\_subset\_1~np\_\_4~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_4~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_4~k1\_numbers))\end{array}
\label{hyp:dhahdgedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_3){\unicdcdcdhd}(m2\_subset\_1~np\_\_3~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_3~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_3~k1\_numbers))\end{array}
\label{hyp:dhahdgddpfogfhngfgchbgmgdh}
\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}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_14){\unicdcdcdhd}(m2\_subset\_1~np\_\_14~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_14~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_14~k1\_numbers))\end{array}
\label{hyp:dhahdgbdedpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_13){\unicdcdcdhd}(m2\_subset\_1~np\_\_13~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_13~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_13~k1\_numbers))\end{array}
\label{hyp:dhahdgbdddpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_12){\unicdcdcdhd}(m2\_subset\_1~np\_\_12~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_12~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_12~k1\_numbers))\end{array}
\label{hyp:dhahdgbdcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_11){\unicdcdcdhd}(m2\_subset\_1~np\_\_11~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_11~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_11~k1\_numbers))\end{array}
\label{hyp:dhahdgbdbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_10){\unicdcdcdhd}(m2\_subset\_1~np\_\_10~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_10~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_10~k1\_numbers))\end{array}
\label{hyp:dhahdgbdadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_9}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchjd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_8}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchid}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_7}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchhd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_6}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchgd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_5}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchfd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_4}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfched}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_3}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_2}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_14}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbded}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_13}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbddd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_12}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbdcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_11}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbdbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_10}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbdad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_1}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{np\_\_15}}~{np\_\_0}}}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdfdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 .  ((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\_partfun1~X1~k5\_numbers))))){\unicdcdcdhd}(v7\_ordinal1~\\
X2))){\unicdbdjdcd}(k3\_compos\_1~X0~X1~X2=k1\_funct\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgpgngahpgdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}(k2\_afinsq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgggjgogdhbhpfbd}
\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}(\preoh v1\_xboole\_0~k4\_scmp\_gcd){\unicdcdcdhd}((v1\_relat\_1~k4\_scmp\_gcd){\unicdcdcdhd}((v4\_relat\_1~\\
k4\_scmp\_gcd~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~k4\_scmp\_gcd~(u1\_compos\_1~\\
k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~k4\_scmp\_gcd){\unicdcdcdhd}((v1\_finset\_1~k4\_scmp\_gcd){\unicdcdcdhd}\\
(v1\_afinsq\_1~k4\_scmp\_gcd))))))\end{array}
\label{hyp:egehpflgedpfdhdgngahpfhgdgeg}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_afinsq\_1~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)))\end{array}
\label{hyp:dgdgjdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgbdfdpfdhdgngahpfhgdgeg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v5\_relat\_1~\\
X0~(u1\_compos\_1~k1\_scmpds\_2)){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_partfun1~\\
X0~k5\_numbers))))){\unicdbdjdcd}((r1\_tarski~k4\_scmp\_gcd~X0){\unicdbdjdcd}((k3\_compos\_1~\\
k1\_scmpds\_2~X0~k6\_numbers=k5\_scmpds\_2~k2\_scmp\_gcd~k6\_numbers){\unicdcdcdhd}\\
((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_1=k5\_scmpds\_2~k3\_scmp\_gcd~np\_\_7){\unicdcdcdhd}\\
((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_2=k6\_scmpds\_2~k3\_scmp\_gcd~k15\_scmpds\_i){\unicdcdcdhd}\\
((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_3=k3\_scmpds\_2~np\_\_2){\unicdcdcdhd}((k3\_compos\_1~\\
k1\_scmpds\_2~X0~np\_\_4=k2\_compos\_1~k1\_scmpds\_2){\unicdcdcdhd}((k3\_compos\_1~\\
k1\_scmpds\_2~X0~np\_\_5=k8\_scmpds\_2~k3\_scmp\_gcd~np\_\_3~np\_\_9){\unicdcdcdhd}((\\
k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_6=k16\_scmpds\_2~k3\_scmp\_gcd~k3\_scmp\_gcd~\\
np\_\_6~np\_\_3){\unicdcdcdhd}((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_7=k15\_scmpds\_2~\\
k3\_scmp\_gcd~k3\_scmp\_gcd~np\_\_2~np\_\_3){\unicdcdcdhd}((k3\_compos\_1~k1\_scmpds\_2~\\
X0~np\_\_8=k16\_scmpds\_2~k3\_scmp\_gcd~k3\_scmp\_gcd~np\_\_7~np\_\_3){\unicdcdcdhd}(\\
(k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_9=k16\_scmpds\_2~k3\_scmp\_gcd~k2\_scmp\_gcd~\\
(k2\_nat\_1~np\_\_4~k14\_scmpds\_i)~np\_\_1){\unicdcdcdhd}((k3\_compos\_1~k1\_scmpds\_2~\\
X0~np\_\_10=k11\_scmpds\_2~k2\_scmp\_gcd~np\_\_1~np\_\_4){\unicdcdcdhd}((k3\_compos\_1~\\
k1\_scmpds\_2~X0~np\_\_11=k6\_scmpds\_2~k3\_scmp\_gcd~k15\_scmpds\_i){\unicdcdcdhd}\\
((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_12=k3\_scmpds\_2~(k4\_xcmplx\_0~\\
np\_\_7)){\unicdcdcdhd}((k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_13=k16\_scmpds\_2~k3\_scmp\_gcd~\\
k3\_scmp\_gcd~np\_\_2~np\_\_6){\unicdcdcdhd}(k3\_compos\_1~k1\_scmpds\_2~X0~np\_\_14=\\
k4\_scmpds\_2~k3\_scmp\_gcd))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
