\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{t70\_fvaluat1 (TMFUdkb5YJrhQhHxT1UrNscHyNiGe1rJ9yE)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_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 $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_realset2~X1){\unicdcdcdhd}(l6\_algstr\_0~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_fvaluat1~\\
X2~X1){\unicdbdjdcd}((v3\_fvaluat1~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k7\_fvaluat1~X1~X2))){\unicdbdjdcd}(k1\_binop\_1~(k4\_group\_1~X1)~X3~X0=k1\_binop\_1~\\
(k4\_group\_1~(k7\_fvaluat1~X1~X2))~X3~X0)))))\end{array}
\label{hyp:ehgdadpfggghbgmgfhbgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}\\
(m1\_subset\_1~(k1\_binop\_1~(k4\_group\_1~X0)~X1~X2)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:mgbdddpffgdgpfahggpfbd}
\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 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\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}
\begin{theorem}\label{thm:ehhdadpfggghbgmgfhbgehbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}\\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_realset2~X1){\unicdcdcdhd}(l6\_algstr\_0~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_fvaluat1~X3~X1){\unicdbdjdcd}(((v3\_fvaluat1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~(k7\_fvaluat1~X1~X3)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_binop\_1~(k4\_group\_1~X1)~X2~X0)~(u1\_struct\_0~(k7\_fvaluat1~X1~\\
X3)))))))\end{array}$$
\end{theorem}
\end{document}
