\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{l17\_pre\_ff (TMJvNrWePvLB6MH5EnhaJn2rN1kbgPLtRhe)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k4\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_abian : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh (\preoh v1\_abian~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~k5\_numbers){\unicdbdjdcd}(X0{\unicdcdgdad}k2\_nat\_1~(k4\_nat\_1~np\_\_2~X1)~np\_\_1))){\unicdcdcdhd}\\
(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}(X0=k2\_nat\_1~(k4\_nat\_1~\\
np\_\_2~X1)~np\_\_1)){\unicdcdcdhd}(v1\_abian~X0)))\end{array}
\label{hyp:ehjdpfbgcgjgbgog}
\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}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\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 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~k5\_numbers)){\unicdbdjdcd}\\
(k1\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}((v1\_abian~X0){\unicdbdjded}({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}(X0=k4\_nat\_1~np\_\_2~X1)))\end{array}
\label{hyp:egcdpfbgcgjgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgbdhdpfahchfgpfgggg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k5\_numbers~\\
(k3\_finseq\_2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~X2~k5\_numbers~\\
(k3\_finseq\_2~k5\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~k5\_numbers~\\
(k3\_finseq\_2~k5\_numbers)){\unicdbdjdcd}(((({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}\\
((k1\_nat\_1~X0~np\_\_2=k4\_nat\_1~np\_\_2~X4){\unicdbdjdcd}(X2=k8\_finseq\_1~k5\_numbers~\\
X1~(k12\_finseq\_1~k5\_numbers~(k7\_partfun1~k5\_numbers~X1~X4))))){\unicdcdcdhd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((k1\_nat\_1~X0~np\_\_2=\\
k2\_nat\_1~(k4\_nat\_1~np\_\_2~X4)~np\_\_1){\unicdbdjdcd}(X2=k8\_finseq\_1~k5\_numbers~\\
X1~(k12\_finseq\_1~k5\_numbers~(k2\_nat\_1~(k7\_partfun1~k5\_numbers~\\
X1~X4)~(k7\_partfun1~k5\_numbers~X1~(k2\_nat\_1~X4~np\_\_1)))))))){\unicdcdcdhd}(\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_numbers){\unicdbdjdcd}((k1\_nat\_1~X0~np\_\_2=\\
k4\_nat\_1~np\_\_2~X4){\unicdbdjdcd}(X3=k8\_finseq\_1~k5\_numbers~X1~(k12\_finseq\_1~\\
k5\_numbers~(k7\_partfun1~k5\_numbers~X1~X4))))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~k5\_numbers){\unicdbdjdcd}((k1\_nat\_1~X0~np\_\_2=k2\_nat\_1~(k4\_nat\_1~np\_\_2~X4)~\\
np\_\_1){\unicdbdjdcd}(X3=k8\_finseq\_1~k5\_numbers~X1~(k12\_finseq\_1~k5\_numbers~\\
(k2\_nat\_1~(k7\_partfun1~k5\_numbers~X1~X4)~(k7\_partfun1~k5\_numbers~\\
X1~(k2\_nat\_1~X4~np\_\_1))))))))){\unicdbdjdcd}(X2=X3)))))\end{array}$$
\end{theorem}
\end{document}
