\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{t11\_prelamb (TMPjHWqMCoSsqjBGSEB4Z6LFwNABJwAUXLj)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_prelamb : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_trees\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_trees\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_trees\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_prelamb : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_prelamb : {{\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\_prelamb~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_prelamb~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v3\_trees\_2~\\
X1))))))\end{array}
\label{hyp:egehpfngbdpfahchfgmgbgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_prelamb~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_trees\_1~X2~(k9\_xtuple\_0~X1)){\unicdbdjdcd}(((k2\_xtuple\_0~(k3\_trees\_2~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))~k5\_numbers)~X1~X2)=k6\_numbers){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((\\
k8\_trees\_2~(k9\_xtuple\_0~X1)~X2=k6\_numbers){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~X0)){\unicdcdcdhd}(k1\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(\\
k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=k4\_tarski~(k12\_finseq\_1~(u1\_struct\_0~X0)~X3)~\\
X3))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~\\
X1~X2)=np\_\_1){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((k8\_trees\_2~(k9\_xtuple\_0~\\
X1)~X2=np\_\_1){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=k4\_tarski~X3~(k2\_prelamb~X0~X4~X5)){\unicdcdcdhd}(k1\_xtuple\_0~\\
(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~\\
k6\_numbers)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~X0)~X3~(k12\_finseq\_1~\\
(u1\_struct\_0~X0)~X5))~X4)))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))~k5\_numbers)~X1~X2)=np\_\_2){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((k8\_trees\_2~\\
(k9\_xtuple\_0~X1)~X2=np\_\_1){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~(k3\_trees\_2~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))~k5\_numbers)~X1~X2)=k4\_tarski~X3~(k1\_prelamb~X0~X5~X4)){\unicdcdcdhd}(k1\_xtuple\_0~\\
(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~\\
k6\_numbers)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k12\_finseq\_1~\\
(u1\_struct\_0~X0)~X5)~X3)~X4)))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))~k5\_numbers)~X1~X2)=np\_\_3){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((k8\_trees\_2~\\
(k9\_xtuple\_0~X1)~X2=np\_\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m2\_finseq\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~\\
(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2)=k4\_tarski~(k8\_finseq\_1~\\
(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(\\
u1\_struct\_0~X0)~X4~(k12\_finseq\_1~(u1\_struct\_0~X0)~(k2\_prelamb~\\
X0~X6~X7)))~X3)~X5)~X8){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~\\
k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~k6\_numbers)))=k4\_tarski~\\
X3~X7){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~\\
(k12\_finseq\_1~k5\_numbers~np\_\_1)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~\\
X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~X4~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~X6))~X5)~X8)))))))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=np\_\_4){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((k8\_trees\_2~\\
(k9\_xtuple\_0~X1)~X2=np\_\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m2\_finseq\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~\\
(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2)=k4\_tarski~(k8\_finseq\_1~\\
(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(\\
u1\_struct\_0~X0)~X4~X3)~(k12\_finseq\_1~(u1\_struct\_0~X0)~(k1\_prelamb~\\
X0~X7~X6)))~X5)~X8){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~\\
X2~(k12\_finseq\_1~k5\_numbers~k6\_numbers)))=k4\_tarski~X3~X7){\unicdcdcdhd}(\\
k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~\\
k5\_numbers~np\_\_1)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~X0)~\\
(k8\_finseq\_1~(u1\_struct\_0~X0)~X4~(k12\_finseq\_1~(u1\_struct\_0~X0)~\\
X6))~X5)~X8)))))))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=np\_\_5){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}((k8\_trees\_2~(k9\_xtuple\_0~\\
X1)~X2=np\_\_1){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m2\_finseq\_1~X7~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((k1\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2)=k4\_tarski~\\
(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~X4~\\
(k12\_finseq\_1~(u1\_struct\_0~X0)~(k3\_prelamb~X0~X5~X6)))~X7)~X3){\unicdcdcdhd}\\
(k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~\\
k5\_numbers~k6\_numbers)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~\\
X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~\\
X4~(k12\_finseq\_1~(u1\_struct\_0~X0)~X5))~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~X6))~X7)~X3)))))))))){\unicdcdcdhd}(((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=np\_\_6){\unicdbdjdcd}((v2\_prelamb~X2~X0~X1){\unicdbdjded}((k8\_trees\_2~\\
(k9\_xtuple\_0~X1)~X2=np\_\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~\\
X1~X2)=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~X0)~X3~X4)~(k3\_prelamb~\\
X0~X5~X6)){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~\\
X2~(k12\_finseq\_1~k5\_numbers~k6\_numbers)))=k4\_tarski~X3~X5){\unicdcdcdhd}(\\
k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~(k12\_finseq\_1~\\
k5\_numbers~np\_\_1)))=k4\_tarski~X4~X6)))))))))){\unicdcdcdhd}(((k2\_xtuple\_0~\\
(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~\\
X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2)=np\_\_7){\unicdbdjdcd}((v2\_prelamb~\\
X2~X0~X1){\unicdbdjded}((k8\_trees\_2~(k9\_xtuple\_0~X1)~X2=np\_\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m2\_finseq\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m2\_finseq\_1~X4~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m2\_finseq\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~\\
X7~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2)=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~X0)~(k8\_finseq\_1~\\
(u1\_struct\_0~X0)~X4~X3)~X5)~X7){\unicdcdcdhd}((k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~\\
k5\_numbers~X2~(k12\_finseq\_1~k5\_numbers~k6\_numbers)))=k4\_tarski~\\
X3~X6){\unicdcdcdhd}(k1\_xtuple\_0~(k1\_funct\_1~X1~(k8\_finseq\_1~k5\_numbers~X2~\\
(k12\_finseq\_1~k5\_numbers~np\_\_1)))=k4\_tarski~(k8\_finseq\_1~(u1\_struct\_0~\\
X0)~(k8\_finseq\_1~(u1\_struct\_0~X0)~X4~(k12\_finseq\_1~(u1\_struct\_0~\\
X0)~X6))~X5)~X7))))))))))){\unicdcdcdhd}(\preoh (k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_1){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_2){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_3){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_4){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_5){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_6){\unicdcdcdhd}((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~\\
k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_7){\unicdcdcdhd}(\preoh (v2\_prelamb~X2~X0~X1){\unicdbdjded}(\preoh True))))))))))))))))))))\end{array}
\label{hyp:egedpfahchfgmgbgngcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_prelamb~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k3\_finseq\_2~(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)){\unicdcdcdhd}\\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v3\_trees\_2~X1))))){\unicdbdjdcd}((m1\_prelamb~\\
X1~X0){\unicdbdjded}((v1\_finset\_1~(k9\_xtuple\_0~X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_trees\_1~\\
X2~(k9\_xtuple\_0~X1)){\unicdbdjdcd}(v2\_prelamb~X2~X0~X1)))))\end{array}
\label{hyp:egbdcdpfahchfgmgbgngcg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfahchfgmgbgngcg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_prelamb~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_prelamb~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_trees\_1~X2~(k9\_xtuple\_0~X1)){\unicdbdjdcd}\\
(\preoh (k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_1){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_2){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_3){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_4){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_5){\unicdcdcdhd}\\
((k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_6){\unicdcdcdhd}\\
(k2\_xtuple\_0~(k3\_trees\_2~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~\\
(u1\_struct\_0~X0))~(u1\_struct\_0~X0))~k5\_numbers)~X1~X2){\unicdcdgdad}np\_\_7))))))))))\end{array}$$
\end{theorem}
\end{document}
