\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{t34\_polyform (TMKkbVMwVCP9kmG5vAMLevYk7Wp3Mfzn1F6)}
\maketitle
Let $ v2\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_polyform : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k11\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k8\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(v2\_funct\_1~\\
(k10\_polyform~X0~X1)))\end{array}
\label{hyp:ehddddpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k4\_finseq\_1~\\
(k10\_polyform~X0~X1)=k2\_finseq\_1~(k11\_polyform~X0~X1)))\end{array}
\label{hyp:ehcdhdpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in k2\_finseq\_1~X1){\unicdbdjded}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~X1))))\end{array}
\label{hyp:ehbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
(k4\_finseq\_1~X0=k9\_xtuple\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}\\
((v4\_polyform~X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_finset\_1~\\
(k8\_polyform~X0~X1))\end{array}
\label{hyp:egehpflgidpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{({{k5\_card\_1}~{X0}})}}~{k4\_ordinal1}})}}}\label{hyp:egehpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}\\
((v4\_polyform~X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}((v1\_relat\_1~\\
(k10\_polyform~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k10\_polyform~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~\\
(k10\_polyform~X0~X1))))\end{array}
\label{hyp:egehpflgbdadpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k11\_polyform~\\
X0~X1=k5\_card\_1~(k8\_polyform~X0~X1)))\end{array}
\label{hyp:egidpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in k9\_xtuple\_0~X0){\unicdcdcdhd}((X2 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(k1\_funct\_1~X0~X1=k1\_funct\_1~X0~X2))){\unicdbdjdcd}(X1=X2)))\end{array}
\label{hyp:egedpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~X2~(k11\_polyform~\\
X0~X1))){\unicdbdjdcd}(k15\_polyform~X0~X1~X2=k1\_funct\_1~(k10\_polyform~X0~X1)~\\
X2))))\end{array}
\label{hyp:egbdcdpfahpgmgjhggpgchng}
\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:ehddedpfahpgmgjhggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X3){\unicdcdcdhd}((r1\_xxreal\_0~X3~(k11\_polyform~X0~X1)){\unicdcdcdhd}((r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}((r1\_xxreal\_0~X2~(k11\_polyform~X0~X1)){\unicdcdcdhd}(k15\_polyform~\\
X0~X1~X3=k15\_polyform~X0~X1~X2))))){\unicdbdjdcd}(X2=X3)))))\end{array}$$
\end{theorem}
\end{document}
