\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{t26\_matrixr1 (TMHiQYUKZSsA1uRaWBMcGUFXQ3vspTUJjXM)}
\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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_matrixr1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~\\
X0))){\unicdbdjdcd}(((k3\_finseq\_1~X1=k3\_finseq\_1~X2){\unicdcdcdhd}(k1\_matrix\_1~X1=k1\_matrix\_1~\\
X2)){\unicdbdjdcd}(k2\_matrix\_1~X1=k2\_matrix\_1~X2)))\end{array}
\label{hyp:ehfdfdpfngbgehchjgihpfed}
\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}\\
((k3\_finseq\_1~(k3\_matrixr1~X0~X1)=k3\_finseq\_1~X0){\unicdcdcdhd}((k1\_matrix\_1~\\
(k3\_matrixr1~X0~X1)=k1\_matrix\_1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}((k4\_tarski~X2~X3 \in k2\_matrix\_1~\\
X0){\unicdbdjdcd}(k3\_matrix\_1~k1\_numbers~(k3\_matrixr1~X0~X1)~X2~X3=k7\_real\_1~\\
(k3\_matrix\_1~k1\_numbers~X0~X2~X3)~(k3\_matrix\_1~k1\_numbers~X1~X2~\\
X3))))))))\end{array}
\label{hyp:ehcdfdpfngbgehchjgihchbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_matrix\_1~\\
X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~X0))){\unicdbdjdcd}(((k3\_finseq\_1~X1=k3\_finseq\_1~\\
X2){\unicdcdcdhd}((k1\_matrix\_1~X1=k1\_matrix\_1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((k4\_tarski~X3~X4 \in k2\_matrix\_1~\\
X1){\unicdbdjdcd}(k3\_matrix\_1~X0~X1~X3~X4=k3\_matrix\_1~X0~X2~X3~X4)))))){\unicdbdjdcd}(X1=\\
X2))))\end{array}
\label{hyp:ehcdbdpfngbgehchjgihpfbd}
\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}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\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~(k3\_matrixr1~X0~X1)){\unicdcdcdhd}(m2\_finseq\_1~\\
(k3\_matrixr1~X0~X1)~(k3\_finseq\_2~k1\_numbers)))\end{array}
\label{hyp:egehpflgddpfngbgehchjgihchbd}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfngbgehchjgihchbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_matrix\_1~X2){\unicdcdcdhd}(m2\_finseq\_1~X2~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(((k3\_finseq\_1~X2=k3\_finseq\_1~X0){\unicdcdcdhd}((k1\_matrix\_1~X2=k1\_matrix\_1~\\
X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}\\
((k4\_tarski~X3~X4 \in k2\_matrix\_1~X0){\unicdbdjdcd}(k3\_matrix\_1~k1\_numbers~X2~\\
X3~X4=k7\_real\_1~(k3\_matrix\_1~k1\_numbers~X0~X3~X4)~(k3\_matrix\_1~\\
k1\_numbers~X1~X3~X4))))))){\unicdbdjdcd}(X2=k3\_matrixr1~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
