\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{t35\_ec\_pf\_2 (TMQW52YK3UroKQLtvSYdc5RpqtvsjLxR3hj)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_binom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k9\_int\_3~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}\\
(k3\_funct\_2~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(k5\_ec\_pf\_1~X0~X1~X2)~(k4\_domain\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~X3~\\
X4~X5)=k5\_algstr\_0~(k9\_int\_3~X0)~(k8\_group\_1~(k9\_int\_3~X0)~(k2\_binom~\\
(k9\_int\_3~X0)~X4~np\_\_2)~X5)~(k3\_rlvect\_1~(k9\_int\_3~X0)~(k3\_rlvect\_1~\\
(k9\_int\_3~X0)~(k2\_binom~(k9\_int\_3~X0)~X3~np\_\_3)~(k8\_group\_1~(k9\_int\_3~\\
X0)~(k8\_group\_1~(k9\_int\_3~X0)~X1~X3)~(k2\_binom~(k9\_int\_3~X0)~X5~np\_\_2)))~\\
(k8\_group\_1~(k9\_int\_3~X0)~X2~(k2\_binom~(k9\_int\_3~X0)~X5~np\_\_3)))))))))\end{array}
\label{hyp:ehedbdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0))~(k6\_ec\_pf\_1~X0~X1~X2)){\unicdbdjdcd}(X3=k4\_domain\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(k4\_ec\_pf\_2~X0~X1~X2~X3)~(k5\_ec\_pf\_2~X0~X1~X2~X3)~(k6\_ec\_pf\_2~\\
X0~X1~X2~X3)))))\end{array}
\label{hyp:ehddbdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k6\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_int\_3~X0))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_ec\_pf\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k6\_ec\_pf\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0)))))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k5\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflgfdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v7\_ordinal1~X0){\unicdcdcdhd}\\
(v1\_int\_2~X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}\\
((m1\_subset\_1~X2~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~\\
(k6\_ec\_pf\_1~X0~X1~X2))))){\unicdbdjdcd}(m1\_subset\_1~(k4\_ec\_pf\_2~X0~X1~X2~X3)~\\
(u1\_struct\_0~(k9\_int\_3~X0)))\end{array}
\label{hyp:egehpflgedpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}(k6\_ec\_pf\_1~X0~X1~X2=ReplSep~(toset~\\
({\uniddcgcg} X3 : \iota .  m2\_subset\_1~X3~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~\\
(k3\_ec\_pf\_1~(k9\_int\_3~X0))))~({\uniddcgcg} X3 : \iota .  k3\_funct\_2~(k3\_zfmisc\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0)))~(u1\_struct\_0~(k9\_int\_3~X0))~(k5\_ec\_pf\_1~X0~X1~X2)~\\
X3=k4\_struct\_0~(k9\_int\_3~X0))~({\uniddcgcg} X3 : \iota .  X3))))\end{array}
\label{hyp:egjdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpffgdgpfahggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0))~(k6\_ec\_pf\_1~X0~X1~X2)){\unicdbdjdcd}(k5\_algstr\_0~(k9\_int\_3~X0)~\\
(k8\_group\_1~(k9\_int\_3~X0)~(k2\_binom~(k9\_int\_3~X0)~(k5\_ec\_pf\_2~\\
X0~X1~X2~X3)~np\_\_2)~(k6\_ec\_pf\_2~X0~X1~X2~X3))~(k3\_rlvect\_1~(k9\_int\_3~\\
X0)~(k3\_rlvect\_1~(k9\_int\_3~X0)~(k2\_binom~(k9\_int\_3~X0)~(k4\_ec\_pf\_2~\\
X0~X1~X2~X3)~np\_\_3)~(k8\_group\_1~(k9\_int\_3~X0)~(k8\_group\_1~(k9\_int\_3~\\
X0)~X1~(k4\_ec\_pf\_2~X0~X1~X2~X3))~(k2\_binom~(k9\_int\_3~X0)~(k6\_ec\_pf\_2~\\
X0~X1~X2~X3)~np\_\_2)))~(k8\_group\_1~(k9\_int\_3~X0)~X2~(k2\_binom~(k9\_int\_3~\\
X0)~(k6\_ec\_pf\_2~X0~X1~X2~X3)~np\_\_3)))=k4\_struct\_0~(k9\_int\_3~X0)))))\end{array}$$
\end{theorem}
\end{document}
