\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{t61\_bvfunc\_1 (TMW42pXdRZhWKwSHARE6iLpUovEA1vFRhmh)}
\maketitle
Let $ v1\_xboolean : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xboolean : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ k2\_xboolean : {\iota}$ be given.
Let $ k1\_xboolean : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k4\_xboolean~\\
X0~(k5\_xboolean~X0~X1)=X0))\end{array}
\label{hyp:ehgdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k5\_xboolean~\\
X0~(k9\_xboolean~X0~X1)=k6\_xboolean~X1~X0))\end{array}
\label{hyp:ehededpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k9\_xboolean~\\
X0~(k4\_xboolean~X0~X1)=k3\_xboolean~X0))\end{array}
\label{hyp:ehddcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k4\_xboolean~\\
X0~(k4\_xboolean~X0~X1)=k4\_xboolean~X0~X1))\end{array}
\label{hyp:ehcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k5\_xboolean~\\
(k3\_xboolean~X0)~(k6\_xboolean~X0~X1)=k6\_xboolean~X0~X1))\end{array}
\label{hyp:ehbdhdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k6\_xboolean~\\
X0~(k6\_xboolean~X0~X1)=k6\_xboolean~X0~X1))\end{array}
\label{hyp:ehbdddpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}((\\
(k4\_xboolean~X0~X1=k8\_margrel1){\unicdbdjdcd}((X0=k8\_margrel1){\unicdcdcdhd}(X1=k8\_margrel1))){\unicdcdcdhd}\\
((((X0=k8\_margrel1){\unicdcdcdhd}(X1=k8\_margrel1)){\unicdbdjdcd}(k4\_xboolean~X0~X1=\\
k8\_margrel1)){\unicdcdcdhd}((\preoh (k4\_xboolean~X0~X1=k7\_margrel1){\unicdcdcdhd}((X0{\unicdcdgdad}k7\_margrel1){\unicdcdcdhd}\\
(X1{\unicdcdgdad}k7\_margrel1))){\unicdcdcdhd}(((X0=k7\_margrel1){\unicdcdcdid}(X1=k7\_margrel1)){\unicdbdjdcd}\\
(k4\_xboolean~X0~X1=k7\_margrel1))))))\end{array}
\label{hyp:ehbdcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}(k5\_xboolean~\\
X0~(k6\_xboolean~X0~X1)=k2\_xboolean))\end{array}
\label{hyp:ehbdcdcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}(((X0=k7\_margrel1){\unicdbdjdcd}(k3\_xboolean~\\
X0=k8\_margrel1)){\unicdcdcdhd}(((k3\_xboolean~X0=k8\_margrel1){\unicdbdjdcd}(X0=k7\_margrel1)){\unicdcdcdhd}\\
(((X0=k8\_margrel1){\unicdbdjdcd}(k3\_xboolean~X0=k7\_margrel1)){\unicdcdcdhd}((k3\_xboolean~\\
X0=k7\_margrel1){\unicdbdjdcd}(X0=k8\_margrel1)))))\end{array}
\label{hyp:ehbdbdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}((\\
k3\_xboolean~X0=k2\_xboolean){\unicdbdjdcd}(k6\_xboolean~X0~X1=k2\_xboolean)))\end{array}
\label{hyp:ehbdbdjdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}(k6\_xboolean~(k6\_xboolean~(k3\_xboolean~\\
X0)~X0)~X0=k2\_xboolean)\end{array}
\label{hyp:ehbdbdidpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}((\\
(k6\_xboolean~X0~X1=k2\_xboolean){\unicdcdcdhd}(k6\_xboolean~X1~X0=k2\_xboolean)){\unicdbdjdcd}\\
(X0=X1)))\end{array}
\label{hyp:ehbdbdgdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_margrel1}={k2\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_xboolean}~{X0}}}\label{hyp:chdgbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboolean}~{X0}})}{\unicdbdjdcd}{({{{k3\_xboolean}~{({{k3\_xboolean}~{X0}})}}={X0}})}}}\label{hyp:jgogghpgmgfhehjgghfgogfgdhdhpflgddpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xboolean~X0){\unicdcdcdhd}(v1\_xboolean~X1)){\unicdbdjdcd}(\\
v1\_xboolean~(k6\_xboolean~X0~X1))\end{array}
\label{hyp:ggdgfdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xboolean~X0){\unicdcdcdhd}(v1\_xboolean~X1)){\unicdbdjdcd}(\\
v1\_xboolean~(k4\_xboolean~X0~X1))\end{array}
\label{hyp:ggdgddpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboolean}~{k2\_xboolean}}\label{hyp:ggdgcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboolean}~{X0}})}{\unicdbdjdcd}{({{v1\_xboolean}~{({{k3\_xboolean}~{X0}})}})}}}\label{hyp:egehpflgddpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboolean}~{X0}})}{\unicdbdjded}{({{({{X0}={k1\_xboolean}})}{\unicdcdcdid}{({{X0}={k2\_xboolean}})}})}}}\label{hyp:egddpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_xboolean}={np\_\_1}}\label{hyp:egcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~X0~X1){\unicdbdjded}(k6\_xboolean~X0~X1=k8\_margrel1)))\end{array}
\label{hyp:egbdpfcgghggfhogdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdbdpfcgghggfhogdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xboolean~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xboolean~X2){\unicdbdjdcd}((r1\_xxreal\_0~X0~(k6\_xboolean~X1~X2)){\unicdbdjded}(r1\_xxreal\_0~\\
(k4\_xboolean~X0~X1)~X2))))\end{array}$$
\end{theorem}
\end{document}
