\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{t9\_robbins4 (TMZH1De4fnHs5kcqeCZcGTa3duVxwA1tdP9)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_robbins4 : {\iota}$ be given.
Let $ k4\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k6\_numbers : {\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 $ k2\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_yellow\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_robbins4 : {\iota}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_robbins1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_robbins1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_robbins1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (u1\_struct\_0~(k2\_yellow\_1~X0)=X0){\unicdcdcdhd}(u1\_orders\_2~(\\
k2\_yellow\_1~X0)=k1\_yellow\_1~X0)\end{array}
\label{hyp:ehbdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(g3\_lattices~X0~X1~X2=g3\_lattices~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}((v3\_orders\_2~(k2\_yellow\_1~\\
X0)){\unicdcdcdhd}((v4\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(v5\_orders\_2~(k2\_yellow\_1~\\
X0))))\end{array}
\label{hyp:ggdgfdpfjhfgmgmgpghhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_lattice3}~{k1\_robbins4}})}{\unicdcdcdhd}{({{v2\_lattice3}~{k1\_robbins4}})}}\label{hyp:ggdgedpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_lattices~X0){\unicdbdjdcd}((v1\_funct\_1~(u2\_lattices~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_lattices~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u2\_lattices~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhcdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_lattices~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_lattices~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_lattices~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_lattices~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_orders\_2~(k2\_yellow\_1~X0)){\unicdcdcdhd}(l1\_orders\_2~(k2\_yellow\_1~\\
X0))\end{array}
\label{hyp:egehpflgcdpfjhfgmgmgpghhpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((v1\_partfun1~(k2\_lattice3~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_relat\_2~\\
(k2\_lattice3~X0)){\unicdcdcdhd}((v4\_relat\_2~(k2\_lattice3~X0)){\unicdcdcdhd}((v8\_relat\_2~\\
(k2\_lattice3~X0)){\unicdcdcdhd}(m1\_subset\_1~(k2\_lattice3~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpflgcdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k14\_lattice3~X0)){\unicdcdcdhd}\\
((v3\_lattices~(k14\_lattice3~X0)){\unicdcdcdhd}((v10\_lattices~(k14\_lattice3~\\
X0)){\unicdcdcdhd}(l3\_lattices~(k14\_lattice3~X0)))))\end{array}
\label{hyp:egehpflgbdedpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_robbins1~X0){\unicdcdcdhd}(l4\_robbins1~X0)){\unicdbdjdcd}((X0=k2\_robbins4){\unicdbdjded}\\
((g3\_lattices~(u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~\\
X0)=k14\_lattice3~k1\_robbins4){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(\\
u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~np\_\_3)){\unicdbdjdcd}\\
((X1=X2){\unicdbdjdcd}(k1\_funct\_1~(u1\_robbins1~X0)~X1=k3\_subset\_1~np\_\_3~X2))))))\end{array}
\label{hyp:egedpfchpgcgcgjgogdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_robbins4=k2\_yellow\_1~(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:egddpfchpgcgcgjgogdhed}
\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}(k3\_lattice3~X0=g1\_orders\_2~(u1\_struct\_0~X0)~(k2\_lattice3~\\
X0))\end{array}
\label{hyp:egcdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}(((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~\\
X0){\unicdcdcdhd}((v5\_orders\_2~X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v3\_lattices~\\
X1){\unicdcdcdhd}((v10\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)))){\unicdbdjdcd}((X1=k14\_lattice3~\\
X0){\unicdbdjded}(g1\_orders\_2~(u1\_struct\_0~X0)~(u1\_orders\_2~X0)=k3\_lattice3~\\
X1))))\end{array}
\label{hyp:egbdfdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}((v3\_lattices~X0){\unicdbdjdcd}(X0=g3\_lattices~\\
(u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~X0){\unicdbdjdcd}(X0=g1\_orders\_2~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfchpgcgcgjgogdhed}
$$\begin{array}{c}u1\_struct\_0~k2\_robbins4=k4\_enumset1~k6\_numbers~np\_\_1~(k6\_subset\_1~\\
np\_\_3~np\_\_1)~np\_\_2~(k6\_subset\_1~np\_\_3~np\_\_2)~np\_\_3\end{array}$$
\end{theorem}
\end{document}
