\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{t36\_hermitan (TMFnJK9npLDhRBcowhbYVfNBM4M2uM4owNp)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_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 $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_complfld : {\iota}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v4\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v2\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_group\_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 $ v6\_struct\_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 $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v8\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X1~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}\\
((v1\_bilinear~X5~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_hermitan~X5~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~(u1\_struct\_0~k1\_complfld)))))))){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~X5~X2~(k5\_algstr\_0~\\
X1~X3~X4)=k5\_algstr\_0~k1\_complfld~(k2\_binop\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~X5~X2~X3)~(k2\_binop\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~X5~\\
X2~X4)))))))\end{array}
\label{hyp:ehddfdpfigfgchngjgehbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~(u1\_struct\_0~X0)){\unicdcdcdhd}((v2\_bilinear~\\
X6~X0~X1~X2){\unicdcdcdhd}((v4\_bilinear~X6~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))~\\
(u1\_struct\_0~X0)))))))){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X2)~(u1\_struct\_0~X0)~X6~(k5\_algstr\_0~X1~X3~X4)~X5=k5\_algstr\_0~X0~\\
(k2\_binop\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)~(u1\_struct\_0~X0)~\\
X6~X3~X5)~(k2\_binop\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)~(u1\_struct\_0~\\
X0)~X6~X4~X5))))))))\end{array}
\label{hyp:ehddfdpfcgjgmgjgogfgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v6\_struct\_0~k1\_complfld){\unicdcdcdhd}((v13\_algstr\_0~k1\_complfld){\unicdcdcdhd}((\\
v33\_algstr\_0~k1\_complfld){\unicdcdcdhd}((v36\_algstr\_0~k1\_complfld){\unicdcdcdhd}((v3\_group\_1~\\
k1\_complfld){\unicdcdcdhd}((v5\_group\_1~k1\_complfld){\unicdcdcdhd}((v3\_vectsp\_1~k1\_complfld){\unicdcdcdhd}\\
((v5\_vectsp\_1~k1\_complfld){\unicdcdcdhd}((v6\_vectsp\_1~k1\_complfld){\unicdcdcdhd}((v2\_rlvect\_1~\\
k1\_complfld){\unicdcdcdhd}((v3\_rlvect\_1~k1\_complfld){\unicdcdcdhd}(v4\_rlvect\_1~k1\_complfld)))))))))))\end{array}
\label{hyp:ggdgddpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k1\_complfld}})}{\unicdcdcdhd}{({{v4\_vectsp\_1}~{k1\_complfld}})}}\label{hyp:ggdgcdpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k1\_complfld}}}})}{\unicdcdcdhd}{({{v36\_algstr\_0}~{k1\_complfld}})}}\label{hyp:ggdgbdpfdgpgngahmgggmgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_vectsp\_1~X1~X0){\unicdbdjdcd}\\
(l2\_algstr\_0~X1))\end{array}
\label{hyp:egehpfmgbdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l2\_algstr\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k5\_algstr\_0~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k1\_complfld}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k1\_complfld}})}}\label{hyp:egehpflgbdpfdgpgngahmgggmgeg}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfigfgchngjgehbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v8\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~\\
X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X1~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X1~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v1\_bilinear~\\
X6~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_bilinear~X6~k1\_complfld~X0~X1){\unicdcdcdhd}((v4\_bilinear~\\
X6~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_hermitan~X6~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X6~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~(u1\_struct\_0~k1\_complfld)))))))))){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~X6~(k5\_algstr\_0~\\
X0~X2~X3)~(k5\_algstr\_0~X1~X4~X5)=k5\_algstr\_0~k1\_complfld~(k5\_algstr\_0~\\
k1\_complfld~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
k1\_complfld)~X6~X2~X4)~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~k1\_complfld)~X6~X2~X5))~(k5\_algstr\_0~k1\_complfld~\\
(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~\\
X6~X3~X4)~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
k1\_complfld)~X6~X3~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
