\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=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t16\_binari\_3 (TMJKiSVg6rnArxVRNH9D2hV9piRi6hgRH1T)}
\maketitle
Let $ k7\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k10\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboolean : {\iota}$ be given.
Let $ k1\_xboolean : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboolean : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_card\_1~X1~X0){\unicdcdcdhd}(m2\_finseq\_1~X1~k6\_margrel1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k6\_margrel1)){\unicdbdjdcd}((k6\_binarith~\\
X0~X1=k6\_binarith~X0~X2){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehcdpfcgjgogbgchjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_card\_1~X1~X0){\unicdcdcdhd}(m2\_finseq\_1~X1~k6\_margrel1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k6\_margrel1)){\unicdbdjdcd}((r1\_binarith~\\
X0~X1~X2){\unicdbdjdcd}(k6\_binarith~X0~(k7\_binarith~X0~X1~X2)=k2\_nat\_1~(k6\_binarith~\\
X0~X1)~(k6\_binarith~X0~X2)))))\end{array}
\label{hyp:ehcdcdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k2\_xcmplx\_0}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehbdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_card\_1~X0~np\_\_1){\unicdcdcdhd}(m2\_finseq\_1~X0~k6\_margrel1)){\unicdbdjdcd}\\
((X0=k12\_finseq\_1~k6\_margrel1~k7\_margrel1){\unicdbdjdcd}(k6\_binarith~np\_\_1~\\
X0=k6\_numbers))\end{array}
\label{hyp:ehbdfdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k6\_margrel1){\unicdbdjdcd}((k8\_binarith~np\_\_1~(k10\_binarith~k6\_margrel1~\\
X0)~(k10\_binarith~k6\_margrel1~X1)=k8\_margrel1){\unicdbdjded}((X0=k8\_margrel1){\unicdcdcdhd}\\
(X1=k8\_margrel1))))\end{array}
\label{hyp:ehbdddpfcgjgogbgchjgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_margrel1}={k2\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_margrel1}={k1\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfogbgehpfbd}
\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}\\
(k12\_finseq\_1~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggjgogdhfgbhpfbd}
\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}\\
(k10\_binarith~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboolean}~{k2\_xboolean}}\label{hyp:ggdgcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k6\_margrel1}}}}\label{hyp:ggdgcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboolean}~{k1\_xboolean}}\label{hyp:ggdgbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~\\
X0)){\unicdcdcdhd}(((v3\_card\_1~X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~k6\_margrel1)){\unicdcdcdhd}((v3\_card\_1~\\
X2~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~k6\_margrel1)))){\unicdbdjdcd}(m1\_subset\_1~(k8\_binarith~\\
X0~X1~X2)~k6\_margrel1)\end{array}
\label{hyp:egehpflgidpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k7\_margrel1}}~{k6\_margrel1}}\label{hyp:egehpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~\\
X0)){\unicdcdcdhd}(((v3\_card\_1~X1~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~k6\_margrel1)){\unicdcdcdhd}((v3\_card\_1~\\
X2~X0){\unicdcdcdhd}(m1\_finseq\_1~X2~k6\_margrel1)))){\unicdbdjdcd}((v3\_card\_1~(k7\_binarith~\\
X0~X1~X2)~X0){\unicdcdcdhd}(m2\_finseq\_1~(k7\_binarith~X0~X1~X2)~k6\_margrel1))\end{array}
\label{hyp:egehpflghdpfcgjgogbgchjgehig}
\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}\\
((v3\_card\_1~(k10\_binarith~X0~X1)~np\_\_1){\unicdcdcdhd}(m2\_finseq\_1~(k10\_binarith~\\
X0~X1)~X0))\end{array}
\label{hyp:egehpflgbdadpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_card\_1~X1~X0){\unicdcdcdhd}(m2\_finseq\_1~X1~k6\_margrel1)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v3\_card\_1~X2~X0){\unicdcdcdhd}(m2\_finseq\_1~X2~k6\_margrel1)){\unicdbdjdcd}((r1\_binarith~\\
X0~X1~X2){\unicdbdjded}(k8\_binarith~X0~X1~X2=k7\_margrel1))))\end{array}
\label{hyp:eghdpfcgjgogbgchjgehig}
\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}
{{k1\_xboolean}={k6\_numbers}}\label{hyp:egbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k6\_margrel1}})}{\unicdbdjdcd}{({{v1\_xboolean}~{X0}})}}}\label{hyp:dgdgcdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboolean}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfihcgpgpgmgfgbgog}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfcgjgogbgchjgpfdd}
$$\begin{array}{c}k7\_binarith~np\_\_1~(k10\_binarith~k6\_margrel1~k7\_margrel1)~(k10\_binarith~\\
k6\_margrel1~k7\_margrel1)=k10\_binarith~k6\_margrel1~k7\_margrel1\end{array}$$
\end{theorem}
\end{document}
