\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{t23\_waybel\_5 (TMYvEAfrcAeokzXYHM1UoQW9HMQWYSji7oz)}
\maketitle
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 $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_waybel\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ u1\_struct\_0 : {{\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_waybel\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_yellow\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_waybel\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_waybel\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}(({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((X4=ReplSep~\\
(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~(u1\_struct\_0~X0)))~({\uniddcgcg} X5 : \\
\iota .  {\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v2\_relat\_1~X6){\unicdcdcdhd}((v4\_relat\_1~\\
X6~X1){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~X1))))){\unicdcdcdhd}((X6 \in k1\_funct\_2~\\
X1~(k5\_finsub\_1~X2)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m2\_pboole~X7~X1~X6~(k7\_funcop\_1~\\
X1~(u1\_struct\_0~X0))){\unicdcdcdhd}(({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X1){\unicdbdjdcd}({\unicdcdadad} X9 .  \\
(X9 \in k1\_funct\_1~X6~X8){\unicdbdjdcd}(k1\_funct\_1~(k1\_waybel\_5~X1~(u1\_struct\_0~\\
X0)~X6~X7~X8)~X9=k1\_binop\_1~X3~X8~X9))){\unicdcdcdhd}(X5=k5\_yellow\_2~X0~(k4\_waybel\_5~\\
X0~X7))))))~({\uniddcgcg} X5 : \iota .  X5)){\unicdbdjdcd}(k5\_yellow\_2~X0~(k4\_waybel\_5~X0~\\
(k6\_waybel\_5~X1~X2~(u1\_struct\_0~X0)~X3))=k1\_yellow\_0~X0~X4)))))){\unicdbdjdcd}\\
(v3\_waybel\_3~X0))\end{array}
\label{hyp:mgddidpfhhbgjhcgfgmgpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((v3\_waybel\_3~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((X4=ReplSep~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)))~({\uniddcgcg} X5 : \iota .  {\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v2\_relat\_1~\\
X6){\unicdcdcdhd}((v4\_relat\_1~X6~X1){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~X1))))){\unicdcdcdhd}\\
((X6 \in k1\_funct\_2~X1~(k5\_finsub\_1~X2)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m2\_pboole~\\
X7~X1~X6~(k7\_funcop\_1~X1~(u1\_struct\_0~X0))){\unicdcdcdhd}(({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~X1){\unicdbdjdcd}({\unicdcdadad} X9 .  (X9 \in k1\_funct\_1~X6~X8){\unicdbdjdcd}(k1\_funct\_1~(k1\_waybel\_5~\\
X1~(u1\_struct\_0~X0)~X6~X7~X8)~X9=k1\_binop\_1~X3~X8~X9))){\unicdcdcdhd}(X5=k5\_yellow\_2~\\
X0~(k4\_waybel\_5~X0~X7))))))~({\uniddcgcg} X5 : \iota .  X5)){\unicdbdjdcd}(k5\_yellow\_2~X0~\\
(k4\_waybel\_5~X0~(k6\_waybel\_5~X1~X2~(u1\_struct\_0~X0)~X3))=k1\_yellow\_0~\\
X0~X4)))))))\end{array}
\label{hyp:mgddhdpfhhbgjhcgfgmgpffd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfhhbgjhcgfgmgpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_orders\_2~X0){\unicdcdcdhd}((v4\_orders\_2~X0){\unicdcdcdhd}((v5\_orders\_2~\\
X0){\unicdcdcdhd}((v1\_lattice3~X0){\unicdcdcdhd}((v2\_lattice3~X0){\unicdcdcdhd}((v3\_lattice3~X0){\unicdcdcdhd}\\
(l1\_orders\_2~X0))))))){\unicdbdjdcd}((v3\_waybel\_3~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X2)~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}((X4=ReplSep~(toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)))~({\uniddcgcg} X5 : \iota .  {\unicdcdaddd} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}((v2\_relat\_1~\\
X6){\unicdcdcdhd}((v4\_relat\_1~X6~X1){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_partfun1~X6~X1))))){\unicdcdcdhd}\\
((X6 \in k1\_funct\_2~X1~(k5\_finsub\_1~X2)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m2\_pboole~\\
X7~X1~X6~(k7\_funcop\_1~X1~(u1\_struct\_0~X0))){\unicdcdcdhd}(({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~X1){\unicdbdjdcd}({\unicdcdadad} X9 .  (X9 \in k1\_funct\_1~X6~X8){\unicdbdjdcd}(k1\_funct\_1~(k1\_waybel\_5~\\
X1~(u1\_struct\_0~X0)~X6~X7~X8)~X9=k1\_binop\_1~X3~X8~X9))){\unicdcdcdhd}(X5=k5\_yellow\_2~\\
X0~(k4\_waybel\_5~X0~X7))))))~({\uniddcgcg} X5 : \iota .  X5)){\unicdbdjdcd}(k5\_yellow\_2~X0~\\
(k4\_waybel\_5~X0~(k6\_waybel\_5~X1~X2~(u1\_struct\_0~X0)~X3))=k1\_yellow\_0~\\
X0~X4)))))))\end{array}$$
\end{theorem}
\end{document}
