\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{t83\_fvaluat1 (TMbULx5mhqFpfR7TzxeZcgNDTw9D2S9csEb)}
\maketitle
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 $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_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 $ v1\_realset2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_fvaluat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_fvaluat1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_fvaluat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_fvaluat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_fvaluat1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}(\\
(v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_realset2~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_fvaluat1~X1~X0){\unicdbdjdcd}((v3\_fvaluat1~\\
X0){\unicdbdjdcd}(k6\_fvaluat1~X0~(k5\_fvaluat1~X0~X1)=k6\_fvaluat1~X0~X1)))\end{array}
\label{hyp:ehidcdpfggghbgmgfhbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_realset2~X0){\unicdcdcdhd}\\
(l6\_algstr\_0~X0)))))))))){\unicdcdcdhd}(m1\_fvaluat1~X1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((\preoh v6\_struct\_0~(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v36\_algstr\_0~(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v3\_group\_1~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v5\_group\_1~(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v4\_vectsp\_1~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v5\_vectsp\_1~(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(k7\_fvaluat1~X0~X1)){\unicdcdcdhd}(l6\_algstr\_0~(k7\_fvaluat1~X0~X1)))))))))))))\end{array}
\label{hyp:egehpflghdpfggghbgmgfhbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_realset2~X0){\unicdcdcdhd}\\
(l6\_algstr\_0~X0)))))))))){\unicdcdcdhd}(m1\_fvaluat1~X1~X0)){\unicdbdjdcd}(m1\_fvaluat1~\\
(k5\_fvaluat1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgfdpfggghbgmgfhbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}(\\
(v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_realset2~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_fvaluat1~X1~X0){\unicdbdjdcd}((v3\_fvaluat1~\\
X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((\preoh v6\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v36\_algstr\_0~X2){\unicdcdcdhd}((v3\_group\_1~X2){\unicdcdcdhd}((v5\_group\_1~X2){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~\\
X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~X2)))))))))))){\unicdbdjdcd}((X2=k7\_fvaluat1~\\
X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k6\_fvaluat1~X0~X1){\unicdcdcdhd}((u1\_algstr\_0~X2=\\
k2\_partfun1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(\\
u1\_struct\_0~X0)~(u1\_algstr\_0~X0)~(k2\_zfmisc\_1~(k6\_fvaluat1~X0~\\
X1)~(k6\_fvaluat1~X0~X1))){\unicdcdcdhd}((u2\_algstr\_0~X2=k2\_partfun1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~X0)~(u2\_algstr\_0~\\
X0)~(k2\_zfmisc\_1~(k6\_fvaluat1~X0~X1)~(k6\_fvaluat1~X0~X1))){\unicdcdcdhd}((u2\_struct\_0~\\
X2=k4\_struct\_0~X0){\unicdcdcdhd}(u3\_struct\_0~X2=k5\_struct\_0~X0)))))))))\end{array}
\label{hyp:egbdcdpfggghbgmgfhbgehbd}
\end{equation}
\begin{theorem}\label{thm:ehidddpfggghbgmgfhbgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}(\\
(v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v1\_realset2~X0){\unicdcdcdhd}(l6\_algstr\_0~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_fvaluat1~X1~X0){\unicdbdjdcd}((v3\_fvaluat1~\\
X0){\unicdbdjdcd}(k7\_fvaluat1~X0~(k5\_fvaluat1~X0~X1)=k7\_fvaluat1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
