\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{t66\_hermitan (TMYrRcuJRqHavPM2AfBYA19BYnLwZEaAjoR)}
\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 $ k10\_bilinear : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ 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 $ 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 .  ((\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}
\begin{theorem}\label{thm:ehgdgdpfigfgchngjgehbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v8\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v9\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}((v10\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}\\
((v11\_vectsp\_1~X0~k1\_complfld){\unicdcdcdhd}(l1\_vectsp\_1~X0~k1\_complfld)))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~k1\_complfld)){\unicdcdcdhd}((v2\_bilinear~\\
X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v4\_bilinear~X1~k1\_complfld~X0~X0){\unicdcdcdhd}((v3\_hermitan~\\
X1~X0){\unicdcdcdhd}((v5\_hermitan~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
k1\_complfld)))))))))){\unicdbdjdcd}(k10\_bilinear~k1\_complfld~(k6\_vectsp10~\\
k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X0~X1))~(k6\_vectsp10~\\
k1\_complfld~X0~(k13\_bilinear~k1\_complfld~X0~X0~X1))~(k8\_hermitan~\\
X0~X1)=k10\_bilinear~k1\_complfld~(k6\_vectsp10~k1\_complfld~X0~(\\
k13\_bilinear~k1\_complfld~X0~X0~X1))~(k6\_vectsp10~k1\_complfld~X0~\\
(k14\_bilinear~k1\_complfld~X0~X0~(k3\_hermitan~X0~X0~X1)))~(k7\_hermitan~\\
X0~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
