\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{t65\_hermitan (TMQhwZXMFxHtKxSXWUEh8Gz6ubZamCURozi)}
\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 $ k6\_vectsp10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_vectsp\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k14\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_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 $ k7\_hermitan : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 .  ((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}(k13\_bilinear~k1\_complfld~X0~X0~X1=k14\_bilinear~\\
k1\_complfld~X0~X0~(k3\_hermitan~X0~X0~X1)))\end{array}
\label{hyp:ehfdgdpfigfgchngjgehbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))))))))){\unicdcdcdhd}(((\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)))))))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~\\
k1\_complfld)){\unicdcdcdhd}((v1\_bilinear~X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_bilinear~\\
X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v4\_bilinear~X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_hermitan~\\
X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~k1\_complfld)))))))))))){\unicdbdjdcd}\\
((v1\_funct\_1~(k7\_hermitan~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k7\_hermitan~\\
X0~X1~X2)~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~X0~\\
(k13\_bilinear~k1\_complfld~X0~X1~X2)))~(u1\_struct\_0~(k6\_vectsp10~\\
k1\_complfld~X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~X0~\\
X1~X2)))))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v1\_bilinear~(k7\_hermitan~\\
X0~X1~X2)~k1\_complfld~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~\\
k1\_complfld~X0~X1~X2))~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}((v2\_bilinear~(k7\_hermitan~\\
X0~X1~X2)~k1\_complfld~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~\\
k1\_complfld~X0~X1~X2))~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}((v4\_bilinear~(k7\_hermitan~\\
X0~X1~X2)~k1\_complfld~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~\\
k1\_complfld~X0~X1~X2))~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}((v2\_hermitan~(k7\_hermitan~\\
X0~X1~X2)~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~\\
X0~X1~X2))~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~k1\_complfld~\\
X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}(m1\_subset\_1~(k7\_hermitan~X0~X1~\\
X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_vectsp10~\\
k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X1~X2)))~(u1\_struct\_0~\\
(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~\\
X0~X1~X2)))))~(u1\_struct\_0~k1\_complfld))))))))))\end{array}
\label{hyp:egehpflghdpfigfgchngjgehbgog}
\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}((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}(k8\_hermitan~X0~X1=k7\_hermitan~X0~X0~X1))\end{array}
\label{hyp:egbdedpfigfgchngjgehbgog}
\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}((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 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v1\_bilinear~\\
X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_bilinear~X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v4\_bilinear~\\
X2~k1\_complfld~X0~X1){\unicdcdcdhd}((v2\_hermitan~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X1))~(u1\_struct\_0~k1\_complfld)))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~\\
X0~(k13\_bilinear~k1\_complfld~X0~X1~X2)))~(u1\_struct\_0~(k6\_vectsp10~\\
k1\_complfld~X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~X0~\\
X1~X2)))))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v1\_bilinear~X3~k1\_complfld~\\
(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X1~X2))~\\
(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~\\
X0~X1~X2)))){\unicdcdcdhd}((v2\_bilinear~X3~k1\_complfld~(k6\_vectsp10~k1\_complfld~\\
X0~(k13\_bilinear~k1\_complfld~X0~X1~X2))~(k6\_vectsp10~k1\_complfld~\\
X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}((\\
v4\_bilinear~X3~k1\_complfld~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~\\
k1\_complfld~X0~X1~X2))~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdcdcdhd}((v2\_hermitan~X3~(k6\_vectsp10~\\
k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X1~X2))~(k6\_vectsp10~\\
k1\_complfld~X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~X0~\\
X1~X2)))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~\\
X0~X1~X2)))~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))))~(u1\_struct\_0~k1\_complfld)))))))))){\unicdbdjdcd}\\
((X3=k7\_hermitan~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X1~X2)))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~\\
X1~(k14\_bilinear~k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2))))){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X1)){\unicdbdjdcd}(((X4=k3\_vectsp\_4~k1\_complfld~X0~X6~(k13\_bilinear~\\
k1\_complfld~X0~X1~X2)){\unicdcdcdhd}(X5=k3\_vectsp\_4~k1\_complfld~X1~X7~(k14\_bilinear~\\
k1\_complfld~X0~X1~(k3\_hermitan~X0~X1~X2)))){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~\\
(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X1~X2)))~\\
(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~X1~(k14\_bilinear~k1\_complfld~\\
X0~X1~(k3\_hermitan~X0~X1~X2))))~(u1\_struct\_0~k1\_complfld)~X3~X4~X5=\\
k2\_binop\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)~(u1\_struct\_0~k1\_complfld)~\\
X2~X6~X7))))))))))\end{array}
\label{hyp:egbdcdpfigfgchngjgehbgog}
\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}((v4\_bilinear~\\
X1~k1\_complfld~X0~X0){\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}(v2\_hermitan~X1~X0~X0)))))\end{array}
\label{hyp:dgdgfdpfigfgchngjgehbgog}
\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}((v2\_bilinear~\\
X1~k1\_complfld~X0~X0){\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}(v1\_bilinear~X1~k1\_complfld~X0~X0)))))\end{array}
\label{hyp:dgdgedpfigfgchngjgehbgog}
\end{equation}
\begin{theorem}\label{thm:ehgdfdpfigfgchngjgehbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v8\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v2\_bilinear~\\
X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v4\_bilinear~X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v3\_hermitan~\\
X1~X0){\unicdcdcdhd}((v5\_hermitan~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
k1\_complfld)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k6\_vectsp10~k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~\\
X0~(k13\_bilinear~k1\_complfld~X0~X0~X1)))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((X2=k3\_vectsp\_4~k1\_complfld~X0~X4~(k13\_bilinear~k1\_complfld~\\
X0~X0~X1)){\unicdcdcdhd}(X3=k3\_vectsp\_4~k1\_complfld~X0~X5~(k13\_bilinear~k1\_complfld~\\
X0~X0~X1))){\unicdbdjdcd}(k2\_binop\_1~(u1\_struct\_0~(k6\_vectsp10~k1\_complfld~\\
X0~(k13\_bilinear~k1\_complfld~X0~X0~X1)))~(u1\_struct\_0~(k6\_vectsp10~\\
k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X0~X1)))~(u1\_struct\_0~\\
k1\_complfld)~(k8\_hermitan~X0~X1)~X2~X3=k2\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~k1\_complfld)~X1~X4~X5)))))))\end{array}$$
\end{theorem}
\end{document}
