\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{t16\_msafree3 (TMZnGR3UzvnpdANSfRbdUqvu657DdUyVnYf)}
\maketitle
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_instalg1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_dtconstr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_trees\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_msaterm : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_msafree3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~\\
X0){\unicdcdcdhd}(l1\_msualg\_1~X0))){\unicdcdcdhd}(((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}\\
((v4\_relat\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~\\
X1~(u1\_struct\_0~X0)))))){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~(u1\_struct\_0~X0))))))){\unicdbdjdcd}\\
(m3\_pboole~(k5\_msafree3~X0~X1~X2)~(u1\_struct\_0~X0)~(u3\_msualg\_1~\\
X0~(k11\_msafree~X0~X1)))\end{array}
\label{hyp:egehpflgfdpfngdhbgggchfgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v1\_instalg1~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v2\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~(u1\_struct\_0~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~(u1\_struct\_0~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m3\_pboole~X3~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~(k11\_msafree~\\
X0~X1))){\unicdbdjdcd}((X3=k5\_msafree3~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_funct\_1~X3~X4=ReplSep~(toset~({\uniddcgcg} X5 : \\
\iota .  m1\_dtconstr~X5~(u1\_struct\_0~(k5\_msafree~X0~X1))~(k5\_trees\_3~\\
(u1\_struct\_0~(k5\_msafree~X0~X1)))~(k1\_msaterm~X0~X1)))~({\uniddcgcg} X5 : \\
\iota .  (k7\_msaterm~X0~X1~X5=X4){\unicdcdcdhd}(r2\_pboole~(u1\_struct\_0~X0)~(k4\_msafree3~\\
X0~X1~X5)~X2))~({\uniddcgcg} X5 : \iota .  X5)))))))\end{array}
\label{hyp:egfdpfngdhbgggchfgfgdd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfngdhbgggchfgfgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v11\_struct\_0~X1){\unicdcdcdhd}((v1\_instalg1~X1){\unicdcdcdhd}\\
(l1\_msualg\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v2\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~(u1\_struct\_0~\\
X1))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdbdjdcd}((X0 \in \\
k1\_funct\_1~(k5\_msafree3~X1~X2~X3)~X4){\unicdbdjdcd}(m1\_dtconstr~X0~(u1\_struct\_0~\\
(k5\_msafree~X1~X2))~(k5\_trees\_3~(u1\_struct\_0~(k5\_msafree~X1~X2)))~\\
(k1\_msaterm~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
