\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{t46\_hermitan (TMTN3rHFX2AZXQarnRU4NjPDHJ1yUxokApQ)}
\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 $ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ v3\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_complex1 : {{\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 $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_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 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
k1\_complfld)){\unicdcdcdhd}((v2\_bilinear~X3~k1\_complfld~X0~X0){\unicdcdcdhd}((v4\_bilinear~\\
X3~k1\_complfld~X0~X0){\unicdcdcdhd}((v3\_hermitan~X3~X0){\unicdcdcdhd}((v5\_hermitan~X3~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)))))))))){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k5\_square\_1~(k17\_complex1~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k1\_complfld)~X3~X1~X2)))~(k3\_xcmplx\_0~(k4\_hermitan~\\
X0~X3~X1)~(k4\_hermitan~X0~X3~X2))))))\end{array}
\label{hyp:ehedfdpfigfgchngjgehbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~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 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v4\_hermitan~\\
X1~X0){\unicdcdcdhd}((v5\_hermitan~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
k1\_complfld)))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k17\_complex1~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k1\_complfld)~X1~X2~X2)=k3\_complex1~(k2\_binop\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~k1\_complfld)~X1~\\
X2~X2)){\unicdcdcdhd}(k4\_hermitan~X0~X1~X2=k17\_complex1~(k2\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~k1\_complfld)~X1~X2~X2)))))\end{array}
\label{hyp:ehedbdpfigfgchngjgehbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{np\_\_1}}~{X0}}={X0}})}}}\label{hyp:ehddpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_vectsp\_1~\\
X0~k1\_complfld)){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)))))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(v1\_xreal\_0~(k4\_hermitan~X0~X1~X2))\end{array}
\label{hyp:egehpflgedpfigfgchngjgehbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)))){\unicdbdjdcd}\\
(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}(v3\_hermitan~\\
X1~X0))){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}(v4\_hermitan~\\
X1~X0)))))\end{array}
\label{hyp:dgdgcdpfigfgchngjgehbgog}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfigfgchngjgehbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v8\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v2\_bilinear~\\
X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v4\_bilinear~X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v3\_hermitan~\\
X1~X0){\unicdcdcdhd}((v5\_hermitan~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
k1\_complfld)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k5\_square\_1~(k17\_complex1~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k1\_complfld)~X1~X2~X3)))~(k8\_real\_1~(k17\_complex1~\\
(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~k1\_complfld)~\\
X1~X2~X2))~(k17\_complex1~(k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~k1\_complfld)~X1~X3~X3)))))))\end{array}$$
\end{theorem}
\end{document}
