\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{t17\_matrixr2 (TMdKuQxMFjSTAWM4PY9JzrvXGeLkYk7yYBw)}
\maketitle
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k6\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\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 $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_matrix\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_matrix\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_matrixr1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_matrixr1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~\\
(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_matrix\_1~X3){\unicdcdcdhd}(m2\_finseq\_1~\\
X3~(k3\_finseq\_2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(((k3\_finseq\_1~X2=k3\_finseq\_1~\\
X3){\unicdcdcdhd}((k1\_matrix\_1~X2=k1\_matrix\_1~X3){\unicdcdcdhd}(k3\_finseq\_1~X1=k1\_matrix\_1~\\
X2))){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X2)~k6\_numbers){\unicdcdcdid}((r1\_xxreal\_0~\\
(k3\_finseq\_1~X1)~k6\_numbers){\unicdcdcdid}(k4\_matrix\_3~X0~(k1\_matrix\_4~X0~\\
X2~X3)~X1=k1\_matrix\_4~X0~(k4\_matrix\_3~X0~X2~X1)~(k4\_matrix\_3~X0~X3~\\
X1))))))))\end{array}
\label{hyp:ehbdgdpfngbgehchjgihchcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_matrix\_1~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~(k3\_finseq\_2~\\
k1\_numbers))){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~\\
k1\_numbers)))){\unicdbdjdcd}((v1\_matrix\_1~(k6\_matrixr1~X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k6\_matrixr1~X0~X1)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflggdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_matrix\_1~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~(k3\_finseq\_2~\\
k1\_numbers))){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~\\
k1\_numbers)))){\unicdbdjdcd}((v1\_matrix\_1~(k5\_matrixr1~X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k5\_matrixr1~X0~X1)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflgfdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}\\
((v5\_group\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(((v1\_matrix\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((v1\_matrix\_1~X2){\unicdcdcdhd}(m1\_finseq\_1~X2~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}((v1\_matrix\_1~(k4\_matrix\_3~X0~X1~X2)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k4\_matrix\_3~X0~X1~X2)~(k3\_finseq\_2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgedpfngbgehchjgihpfdd}
\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 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
((v1\_matrix\_1~(k1\_matrixr1~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k1\_matrixr1~X0)~\\
(k3\_finseq\_2~(u1\_struct\_0~k2\_vectsp\_1))))\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}\\
((v5\_group\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(((v1\_matrix\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))){\unicdcdcdhd}((v1\_matrix\_1~X2){\unicdcdcdhd}(m1\_finseq\_1~X2~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}((v1\_matrix\_1~(k1\_matrix\_4~X0~X1~X2)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k1\_matrix\_4~X0~X1~X2)~(k3\_finseq\_2~(u1\_struct\_0~X0))))\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(k6\_matrixr1~X0~X1=k2\_matrixr1~(k4\_matrix\_3~k2\_vectsp\_1~(k1\_matrixr1~\\
X0)~(k1\_matrixr1~X1))))\end{array}
\label{hyp:eggdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(k5\_matrixr1~X0~X1=k2\_matrixr1~(k1\_matrix\_4~k2\_vectsp\_1~(k1\_matrixr1~\\
X0)~(k1\_matrixr1~X1))))\end{array}
\label{hyp:egfdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~(u1\_struct\_0~\\
k2\_vectsp\_1)))){\unicdbdjdcd}(k2\_matrixr1~X0=X0)\end{array}
\label{hyp:egcdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(k1\_matrixr1~X0=X0)\end{array}
\label{hyp:egbdpfngbgehchjgihchbd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfngbgehchjgihchcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(((k3\_finseq\_1~X0=k3\_finseq\_1~X1){\unicdcdcdhd}((k1\_matrix\_1~X0=k1\_matrix\_1~\\
X1){\unicdcdcdhd}(k3\_finseq\_1~X2=k1\_matrix\_1~X0))){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~\\
X0)~k6\_numbers){\unicdcdcdid}((r1\_xxreal\_0~(k3\_finseq\_1~X2)~k6\_numbers){\unicdcdcdid}\\
(k6\_matrixr1~(k5\_matrixr1~X0~X1)~X2=k5\_matrixr1~(k6\_matrixr1~\\
X0~X2)~(k6\_matrixr1~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
