\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{t28\_prelamb (TMEjxuyq44nCNuMMKfag2QA6ekeiQ8jCErU)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_prelamb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_prelamb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_prelamb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_prelamb}~{X0}})}{\unicdbdjdcd}{({{l1\_prelamb}~{X0}})}}}\label{hyp:egehpfmgcdpfahchfgmgbgngcg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_prelamb}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgmgbgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_prelamb~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k3\_prelamb~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgddpfahchfgmgbgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_1~(k12\_finseq\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_prelamb~X0)){\unicdbdjdcd}((v10\_prelamb~\\
X0){\unicdbdjded}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(r2\_prelamb~\\
X0~(k12\_finseq\_1~(u1\_struct\_0~X0)~X1)~X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_prelamb~\\
X0~(k8\_finseq\_1~(u1\_struct\_0~X0)~X1~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~X3))~X2){\unicdbdjdcd}(r2\_prelamb~X0~X1~(k2\_prelamb~X0~X2~X3)))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((r2\_prelamb~X0~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k12\_finseq\_1~(\\
u1\_struct\_0~X0)~X3)~X1)~X2){\unicdbdjdcd}(r2\_prelamb~X0~X1~(k1\_prelamb~X0~X3~X2)))))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(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 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_prelamb~X0~X1~X5){\unicdcdcdhd}(r2\_prelamb~X0~(k8\_finseq\_1~\\
(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~X2~(k12\_finseq\_1~\\
(u1\_struct\_0~X0)~X4))~X3)~X6)){\unicdbdjdcd}(r2\_prelamb~X0~(k8\_finseq\_1~(u1\_struct\_0~\\
X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~\\
X2~(k12\_finseq\_1~(u1\_struct\_0~X0)~(k2\_prelamb~X0~X4~X5)))~X1)~X3)~\\
X6)))))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(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 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_prelamb~X0~X1~X5){\unicdcdcdhd}(r2\_prelamb~\\
X0~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~\\
X2~(k12\_finseq\_1~(u1\_struct\_0~X0)~X4))~X3)~X6)){\unicdbdjdcd}(r2\_prelamb~X0~\\
(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(\\
k8\_finseq\_1~(u1\_struct\_0~X0)~X2~X1)~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~(k1\_prelamb~X0~X5~X4)))~X3)~X6)))))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_prelamb~X0~(k8\_finseq\_1~(u1\_struct\_0~\\
X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~\\
X1~(k12\_finseq\_1~(u1\_struct\_0~X0)~X3))~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~X4))~X2)~X5){\unicdbdjdcd}(r2\_prelamb~X0~(k8\_finseq\_1~(u1\_struct\_0~X0)~(\\
k8\_finseq\_1~(u1\_struct\_0~X0)~X1~(k12\_finseq\_1~(u1\_struct\_0~X0)~\\
(k3\_prelamb~X0~X3~X4)))~X2)~X5))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_finseq\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_prelamb~X0~X1~X3){\unicdcdcdhd}(r2\_prelamb~\\
X0~X2~X4)){\unicdbdjdcd}(r2\_prelamb~X0~(k8\_finseq\_1~(u1\_struct\_0~X0)~X1~X2)~(\\
k3\_prelamb~X0~X3~X4))))))))))))))\end{array}
\label{hyp:egbdidpfahchfgmgbgngcg}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfahchfgmgbgngcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_prelamb~X0){\unicdcdcdhd}(l2\_prelamb~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_prelamb~X0~(k12\_finseq\_1~\\
(u1\_struct\_0~X0)~X1)~(k2\_prelamb~X0~(k3\_prelamb~X0~X1~X2)~X2)){\unicdcdcdhd}(\\
r2\_prelamb~X0~(k12\_finseq\_1~(u1\_struct\_0~X0)~X1)~(k1\_prelamb~X0~\\
X2~(k3\_prelamb~X0~X2~X1))))))\end{array}$$
\end{theorem}
\end{document}
