\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{t25\_rlvect\_x (TMXc7yEmDqRG4VSKyrb6Sgii9sS3d3FvsfD)}
\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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_rlvect\_x : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_seq\_1 : {{\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}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \preoh (X2 \in k2\_rlvect\_x~X0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_finseq\_1~\\
X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v5\_relat\_1~X5~k4\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X5){\unicdcdcdhd}(v1\_finseq\_1~X5)))){\unicdbdjdcd}(\preoh (X2=k4\_rlvect\_1~X0~X4){\unicdcdcdhd}\\
((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X0)~X3)~X1){\unicdcdcdhd}((k3\_finseq\_1~\\
X3=k3\_finseq\_1~X4){\unicdcdcdhd}((k3\_finseq\_1~X3=k3\_finseq\_1~X5){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(v7\_ordinal1~X6){\unicdbdjdcd}((X6 \in k2\_finseq\_1~(k3\_finseq\_1~X3)){\unicdbdjdcd}(k7\_partfun1~\\
(u1\_struct\_0~X0)~X4~X6=k1\_rlvect\_1~X0~(k7\_partfun1~(u1\_struct\_0~\\
X0)~X3~X6)~(k1\_seq\_1~X5~X6)))))))))))))\end{array}
\label{hyp:mgcdjdpfchmgghfgdgehpfih}
\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}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}\\
((v5\_relat\_1~X4~k4\_numbers){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~X4)))){\unicdbdjdcd}\\
(((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X0)~X2)~X1){\unicdcdcdhd}((k3\_finseq\_1~\\
X2=k3\_finseq\_1~X3){\unicdcdcdhd}((k3\_finseq\_1~X2=k3\_finseq\_1~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
(v7\_ordinal1~X5){\unicdbdjdcd}((X5 \in k2\_finseq\_1~(k3\_finseq\_1~X2)){\unicdbdjdcd}(k7\_partfun1~\\
(u1\_struct\_0~X0)~X3~X5=k1\_rlvect\_1~X0~(k7\_partfun1~(u1\_struct\_0~\\
X0)~X2~X5)~(k1\_seq\_1~X4~X5))))))){\unicdbdjdcd}(k4\_rlvect\_1~X0~X3 \in k2\_rlvect\_x~\\
X0~X1))))))\end{array}
\label{hyp:mgcdidpfchmgghfgdgehpfih}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfchmgghfgdgehpfih}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k2\_rlvect\_x~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_finseq\_1~\\
X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}((v5\_relat\_1~X5~k4\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X5){\unicdcdcdhd}(v1\_finseq\_1~X5)))){\unicdcdcdhd}((X2=k4\_rlvect\_1~X0~X4){\unicdcdcdhd}\\
((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~X0)~X3)~X1){\unicdcdcdhd}((k3\_finseq\_1~\\
X3=k3\_finseq\_1~X4){\unicdcdcdhd}((k3\_finseq\_1~X3=k3\_finseq\_1~X5){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(v7\_ordinal1~X6){\unicdbdjdcd}((X6 \in k2\_finseq\_1~(k3\_finseq\_1~X3)){\unicdbdjdcd}(k7\_partfun1~\\
(u1\_struct\_0~X0)~X4~X6=k1\_rlvect\_1~X0~(k7\_partfun1~(u1\_struct\_0~\\
X0)~X3~X6)~(k1\_seq\_1~X5~X6)))))))))))))\end{array}$$
\end{theorem}
\end{document}
