\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=}
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\newcommand\unicdcdcdjd{\cap}
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\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{t69\_fvsum\_1 (TMErQWMX3WJz6vv7BjXhhf9mnkA1eL1uX2E)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_fvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k12\_fvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~(u1\_struct\_0~\\
X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~\\
X4~(u1\_struct\_0~X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~X1))){\unicdbdjdcd}(k10\_fvsum\_1~\\
X0~X1~(k12\_fvsum\_1~X0~X1~X3~X4)~X2=k12\_fvsum\_1~X0~X1~(k10\_fvsum\_1~\\
X0~X1~X3~X2)~X4)))))\end{array}
\label{hyp:ehgdidpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~(u1\_struct\_0~X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_finseq\_2~X3~(u1\_struct\_0~X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}(k12\_fvsum\_1~X0~X1~X2~X3=k12\_fvsum\_1~X0~X1~X3~X2))))\end{array}
\label{hyp:ehgdddpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X0){\unicdbdjdcd}(m1\_finseq\_2~(k4\_finseq\_2~\\
X0~X1)~X1)\end{array}
\label{hyp:egehpflgedpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X0~\\
k5\_numbers){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdcdcdhd}((m1\_subset\_1~\\
X2~(k4\_finseq\_2~X0~(u1\_struct\_0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}(m2\_finseq\_2~(k10\_fvsum\_1~X0~X1~X2~X3)~(u1\_struct\_0~X1)~\\
(k4\_finseq\_2~X0~(u1\_struct\_0~X1)))\end{array}
\label{hyp:egehpflgbdadpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehgdjdpfggghdhfhngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v5\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~\\
X3~(u1\_struct\_0~X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m2\_finseq\_2~X4~(u1\_struct\_0~X1)~(k4\_finseq\_2~X0~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}((k10\_fvsum\_1~X0~X1~(k12\_fvsum\_1~X0~X1~X3~X4)~X2=k12\_fvsum\_1~\\
X0~X1~(k10\_fvsum\_1~X0~X1~X3~X2)~X4){\unicdcdcdhd}(k10\_fvsum\_1~X0~X1~(k12\_fvsum\_1~\\
X0~X1~X3~X4)~X2=k12\_fvsum\_1~X0~X1~X3~(k10\_fvsum\_1~X0~X1~X4~X2)))))))\end{array}$$
\end{theorem}
\end{document}
