\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{t29\_robbins4 (TMWicUyKVnnryWMjyta3HM64MLRbSgushhq)}
\maketitle
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_robbins4 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_robbins1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_robbins1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_robbins1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}u1\_struct\_0~k2\_robbins4=k4\_enumset1~k6\_numbers~np\_\_1~(k6\_subset\_1~\\
np\_\_3~np\_\_1)~np\_\_2~(k6\_subset\_1~np\_\_3~np\_\_2)~np\_\_3\end{array}
\label{hyp:ehjdpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k2\_robbins4)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~k2\_robbins4)){\unicdbdjdcd}((X0=k6\_numbers){\unicdbdjdcd}\\
(k3\_lattices~k2\_robbins4~X0~X1=X1)))\end{array}
\label{hyp:ehcdgdpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_lattices~X0~X1~X2=X2)){\unicdbdjdcd}\\
(X1=k5\_lattices~X0)))\end{array}
\label{hyp:ehbdedpfmgbgehehjgdgfgcd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v10\_lattices}~{k2\_robbins4}})}{\unicdcdcdhd}{({{v4\_robbins1}~{k2\_robbins4}})}}\label{hyp:ggdggdpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k2\_robbins4}}}})}{\unicdcdcdhd}{({{v4\_robbins1}~{k2\_robbins4}})}}\label{hyp:ggdgfdpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_robbins1}~{X0}})}{\unicdbdjdcd}{({{({{l2\_robbins1}~{X0}})}{\unicdcdcdhd}{({{l3\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgedpfchpgcgcgjgogdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v4\_robbins1}~{k2\_robbins4}})}{\unicdcdcdhd}{({{l4\_robbins1}~{k2\_robbins4}})}}\label{hyp:egehpflgcdpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  (X6=k4\_enumset1~X0~X1~X2~X3~X4~X5){\unicdbdjded}({\unicdcdadad} X7 .  (X7 \in X6){\unicdbdjded}\\
(\preoh (X7{\unicdcdgdad}X0){\unicdcdcdhd}((X7{\unicdcdgdad}X1){\unicdcdcdhd}((X7{\unicdcdgdad}X2){\unicdcdcdhd}((X7{\unicdcdgdad}X3){\unicdcdcdhd}((X7{\unicdcdgdad}X4){\unicdcdcdhd}(X7{\unicdcdgdad}X5)))))))\end{array}
\label{hyp:egedpffgogfhngdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfchpgcgcgjgogdhed}
${{{k5\_lattices}~{k2\_robbins4}}={k6\_numbers}}$.
\end{theorem}
\end{document}
