\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{t10\_matrix12 (TMKGDTqdvfvYxejinHxokj3jz3UBqzkwLYN)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ m1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix12 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_matrix\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 .  \\
((v7\_ordinal1~X0){\unicdcdcdhd}((v7\_ordinal1~X1){\unicdcdcdhd}(((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\\
\preoh v6\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~\\
X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}(\\
(v4\_rlvect\_1~X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~\\
X2)))))))))))){\unicdcdcdhd}((m1\_matrix\_1~X3~(u1\_struct\_0~X2)~X0~X1){\unicdcdcdhd}((v7\_ordinal1~\\
X4){\unicdcdcdhd}(v7\_ordinal1~X5)))))){\unicdbdjdcd}(m1\_matrix\_1~(k1\_matrix12~X0~X1~X2~\\
X3~X4~X5)~(u1\_struct\_0~X2)~X0~X1)\end{array}
\label{hyp:egehpflgbdpfngbgehchjgihbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v6\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}(\\
(v33\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}((v2\_rlvect\_1~\\
X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}\\
((v5\_vectsp\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_matrix\_1~X3~(u1\_struct\_0~X2)~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~\\
X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_matrix\_1~X6~\\
(u1\_struct\_0~X2)~X0~X1){\unicdbdjdcd}((X6=k1\_matrix12~X0~X1~X2~X3~X4~X5){\unicdbdjded}((k3\_finseq\_1~\\
X6=k3\_finseq\_1~X3){\unicdcdcdhd}({\unicdcdadad} X7 .  (v7\_ordinal1~X7){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(v7\_ordinal1~X8){\unicdbdjdcd}(((X7 \in k4\_finseq\_1~X3){\unicdcdcdhd}(X8 \in k2\_finseq\_1~(k1\_matrix\_1~\\
X3))){\unicdbdjdcd}(((X7=X4){\unicdbdjdcd}(k3\_matrix\_1~(u1\_struct\_0~X2)~X6~X7~X8=k3\_matrix\_1~\\
(u1\_struct\_0~X2)~X3~X5~X8)){\unicdcdcdhd}(((X7=X5){\unicdbdjdcd}(k3\_matrix\_1~(u1\_struct\_0~\\
X2)~X6~X7~X8=k3\_matrix\_1~(u1\_struct\_0~X2)~X3~X4~X8)){\unicdcdcdhd}(\preoh (X7{\unicdcdgdad}X4){\unicdcdcdhd}\\
((X7{\unicdcdgdad}X5){\unicdcdcdhd}(k3\_matrix\_1~(u1\_struct\_0~X2)~X6~X7~X8{\unicdcdgdad}k3\_matrix\_1~(\\
u1\_struct\_0~X2)~X3~X7~X8))))))))))))))))\end{array}
\label{hyp:egbdpfngbgehchjgihbdcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfngbgehchjgihbdcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (\\
(\preoh v2\_struct\_0~X4){\unicdcdcdhd}((\preoh v6\_struct\_0~X4){\unicdcdcdhd}((v13\_algstr\_0~X4){\unicdcdcdhd}((\\
v33\_algstr\_0~X4){\unicdcdcdhd}((v3\_group\_1~X4){\unicdcdcdhd}((v5\_group\_1~X4){\unicdcdcdhd}((v2\_rlvect\_1~\\
X4){\unicdcdcdhd}((v3\_rlvect\_1~X4){\unicdcdcdhd}((v4\_rlvect\_1~X4){\unicdcdcdhd}((v4\_vectsp\_1~X4){\unicdcdcdhd}\\
((v5\_vectsp\_1~X4){\unicdcdcdhd}(l6\_algstr\_0~X4)))))))))))){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_matrix\_1~X5~(u1\_struct\_0~X4)~X0~X1){\unicdbdjdcd}(k1\_matrix12~X0~X1~X4~X5~\\
X2~X3=k1\_matrix12~X0~X1~X4~X5~X3~X2))))))\end{array}$$
\end{theorem}
\end{document}
