\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{t6\_lang1 (TMRVo2jyz2bCv1R2J5Qmd4C83Kzr5wQsDAj)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lang1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_lang1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}((X1=k9\_finseq\_1~X0){\unicdbdjded}((k3\_finseq\_1~X1=np\_\_1){\unicdcdcdhd}(k1\_funct\_1~\\
X1~np\_\_1=X0)))\end{array}
\label{hyp:ehedadpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_finseq\_1}~{({{k5\_finseq\_1}~{X0}})}}}\label{hyp:ggdghdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k5\_finseq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k5\_finseq\_1~\\
X0))\end{array}
\label{hyp:ggdggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((r3\_lang1~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finseq\_1~X3))){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X3)){\unicdcdcdhd}\\
((k1\_funct\_1~X3~np\_\_1=X1){\unicdcdcdhd}((k1\_funct\_1~X3~(k3\_finseq\_1~X3)=X2){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~\\
X4){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X3)~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m2\_finseq\_2~\\
X5~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m2\_finseq\_2~X6~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(\preoh (k1\_funct\_1~X3~X4=X5){\unicdcdcdhd}((k1\_funct\_1~X3~(k2\_nat\_1~X4~np\_\_1)=X6){\unicdcdcdhd}\\
(r2\_lang1~X0~X5~X6)))))))))))))))\end{array}
\label{hyp:egfdpfmgbgoghgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfmgbgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lang1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~\\
X1~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}(r3\_lang1~\\
X0~X1~X1))\end{array}$$
\end{theorem}
\end{document}
