\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{t19\_matrtop3 (TMKkaN7ywDrEkSGuY4FYXW65PecU1YmNLSd)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v4\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_matrtop3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Let $ k5\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrix\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdcdcdid}(k5\_matrix\_6~\\
X3~k2\_vectsp\_1~(k2\_matrtop3~X3~X0~X1~X2)=k2\_matrtop3~X3~(k4\_xcmplx\_0~\\
X0)~X1~X2))))))\end{array}
\label{hyp:mgcdgdpfngbgehchehpgahdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdcdcdid}(k5\_matrix\_1~\\
X3~(u1\_struct\_0~k2\_vectsp\_1)~(k2\_matrtop3~X3~X0~X1~X2)=k2\_matrtop3~\\
X3~(k4\_xcmplx\_0~X0)~X1~X2))))))\end{array}
\label{hyp:mgcdedpfngbgehchehpgahdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v6\_struct\_0~k2\_vectsp\_1){\unicdcdcdhd}((v13\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((\\
v33\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((v36\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((v2\_rlvect\_1~\\
k2\_vectsp\_1){\unicdcdcdhd}((v3\_rlvect\_1~k2\_vectsp\_1){\unicdcdcdhd}((v4\_rlvect\_1~k2\_vectsp\_1){\unicdcdcdhd}\\
((v3\_group\_1~k2\_vectsp\_1){\unicdcdcdhd}((v5\_group\_1~k2\_vectsp\_1){\unicdcdcdhd}((v3\_vectsp\_1~\\
k2\_vectsp\_1){\unicdcdcdhd}((v5\_vectsp\_1~k2\_vectsp\_1){\unicdcdcdhd}(v6\_vectsp\_1~k2\_vectsp\_1)))))))))))\end{array}
\label{hyp:ggdgidpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}{\unicdcdcdhd}{({{v4\_vectsp\_1}~{k2\_vectsp\_1}})}}\label{hyp:ggdggdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k2\_vectsp\_1}}}})}{\unicdcdcdhd}{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}}\label{hyp:ggdgedpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k2\_vectsp\_1}})}}\label{hyp:egehpflgcdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v7\_ordinal1~X0){\unicdcdcdhd}\\
((v1\_xreal\_0~X1){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X3)))){\unicdbdjdcd}((v1\_matrix\_6~\\
(k2\_matrtop3~X0~X1~X2~X3)~X0~k2\_vectsp\_1){\unicdcdcdhd}(m1\_matrix\_1~(k2\_matrtop3~\\
X0~X1~X2~X3)~(u1\_struct\_0~k2\_vectsp\_1)~X0~X0))\end{array}
\label{hyp:egehpflgcdpfngbgehchehpgahdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v33\_algstr\_0~X1){\unicdcdcdhd}(\\
(v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~\\
X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}\\
(l6\_algstr\_0~X1)))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_matrix\_1~X2~(u1\_struct\_0~\\
X1)~X0~X0){\unicdbdjdcd}((v4\_matrix\_6~X2~X0~X1){\unicdbdjded}((v1\_matrix\_6~X2~X0~X1){\unicdcdcdhd}(k5\_matrix\_1~\\
X0~(u1\_struct\_0~X1)~X2=k5\_matrix\_6~X0~X1~X2)))))\end{array}
\label{hyp:eghdpfngbgehchjgihpfgd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfngbgehchehpgahdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~X2~X3)){\unicdbdjdcd}((r1\_xxreal\_0~X2~X1){\unicdcdcdid}((v4\_matrix\_6~\\
(k2\_matrtop3~X3~X0~X1~X2)~X3~k2\_vectsp\_1){\unicdcdcdhd}(k5\_matrix\_6~X3~k2\_vectsp\_1~\\
(k2\_matrtop3~X3~X0~X1~X2)=k2\_matrtop3~X3~(k4\_xcmplx\_0~X0)~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
