\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{t49\_polyform (TMKtx6zPydgetmbz6BXYVWGgKfGVjZN7Z5d)}
\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 $ k1\_vectsp\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_bspace : {\iota}$ be given.
Let $ k17\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ranknull : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k21\_polyform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_ranknull : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_matrlin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}((v9\_vectsp\_1~\\
X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~X0){\unicdcdcdhd}((v1\_matrlin~\\
X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}\\
((v4\_rlvect\_1~X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}((v1\_matrlin~X2~X0){\unicdcdcdhd}\\
(l1\_vectsp\_1~X2~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}((v13\_vectsp\_1~\\
X3~X1~X2){\unicdcdcdhd}((v1\_mod\_2~X3~X0~X1~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)))))))){\unicdbdjdcd}(k1\_vectsp\_9~\\
X0~X1=k2\_xcmplx\_0~(k10\_ranknull~X0~X1~X2~X3)~(k11\_ranknull~X0~X1~\\
X2~X3)))))\end{array}
\label{hyp:ehededpfchbgoglgogfhmgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\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 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfjgogehpfbd}
\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\_funct\_1~\\
(k21\_polyform~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k21\_polyform~X0~X1)~(u1\_struct\_0~\\
(k17\_polyform~X0~X1))~(u1\_struct\_0~(k17\_polyform~X0~(k6\_xcmplx\_0~\\
X1~np\_\_1)))){\unicdcdcdhd}((v13\_vectsp\_1~(k21\_polyform~X0~X1)~(k17\_polyform~\\
X0~X1)~(k17\_polyform~X0~(k6\_xcmplx\_0~X1~np\_\_1))){\unicdcdcdhd}(v1\_mod\_2~(k21\_polyform~\\
X0~X1)~k2\_bspace~(k17\_polyform~X0~X1)~(k17\_polyform~X0~(k6\_xcmplx\_0~\\
X1~np\_\_1))))))\end{array}
\label{hyp:ggdgbdpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k2\_bspace){\unicdcdcdhd}((\preoh v6\_struct\_0~k2\_bspace){\unicdcdcdhd}((v13\_algstr\_0~\\
k2\_bspace){\unicdcdcdhd}((v33\_algstr\_0~k2\_bspace){\unicdcdcdhd}((v3\_group\_1~k2\_bspace){\unicdcdcdhd}\\
((v5\_group\_1~k2\_bspace){\unicdcdcdhd}((v4\_vectsp\_1~k2\_bspace){\unicdcdcdhd}((v5\_vectsp\_1~\\
k2\_bspace){\unicdcdcdhd}((v2\_rlvect\_1~k2\_bspace){\unicdcdcdhd}((v3\_rlvect\_1~k2\_bspace){\unicdcdcdhd}\\
((v4\_rlvect\_1~k2\_bspace){\unicdcdcdhd}(l6\_algstr\_0~k2\_bspace)))))))))))\end{array}
\label{hyp:egehpflgcdpfcgdhahbgdgfg}
\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\_funct\_1~\\
(k21\_polyform~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k21\_polyform~X0~X1)~(u1\_struct\_0~\\
(k17\_polyform~X0~X1))~(u1\_struct\_0~(k17\_polyform~X0~(k6\_xcmplx\_0~\\
X1~np\_\_1)))){\unicdcdcdhd}(m1\_subset\_1~(k21\_polyform~X0~X1)~(k1\_zfmisc\_1~(\\
k2\_zfmisc\_1~(u1\_struct\_0~(k17\_polyform~X0~X1))~(u1\_struct\_0~(\\
k17\_polyform~X0~(k6\_xcmplx\_0~X1~np\_\_1))))))))\end{array}
\label{hyp:egehpflgcdbdpfahpgmgjhggpgchng}
\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}((\preoh v2\_struct\_0~\\
(k17\_polyform~X0~X1)){\unicdcdcdhd}((v13\_algstr\_0~(k17\_polyform~X0~X1)){\unicdcdcdhd}(\\
(v8\_vectsp\_1~(k17\_polyform~X0~X1)~k2\_bspace){\unicdcdcdhd}((v9\_vectsp\_1~(\\
k17\_polyform~X0~X1)~k2\_bspace){\unicdcdcdhd}((v10\_vectsp\_1~(k17\_polyform~\\
X0~X1)~k2\_bspace){\unicdcdcdhd}((v11\_vectsp\_1~(k17\_polyform~X0~X1)~k2\_bspace){\unicdcdcdhd}\\
((v2\_rlvect\_1~(k17\_polyform~X0~X1)){\unicdcdcdhd}((v3\_rlvect\_1~(k17\_polyform~\\
X0~X1)){\unicdcdcdhd}((v4\_rlvect\_1~(k17\_polyform~X0~X1)){\unicdcdcdhd}((v1\_matrlin~(k17\_polyform~\\
X0~X1)~k2\_bspace){\unicdcdcdhd}(l1\_vectsp\_1~(k17\_polyform~X0~X1)~k2\_bspace)))))))))))\end{array}
\label{hyp:egehpflgbdhdpfahpgmgjhggpgchng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgcdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfahpgmgjhggpgchng}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_polyform~X0){\unicdcdcdhd}((v3\_polyform~X0){\unicdcdcdhd}((v4\_polyform~\\
X0){\unicdcdcdhd}(l1\_polyform~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}(k1\_vectsp\_9~\\
k2\_bspace~(k17\_polyform~X0~X1)=k2\_xcmplx\_0~(k10\_ranknull~k2\_bspace~\\
(k17\_polyform~X0~X1)~(k17\_polyform~X0~(k6\_xcmplx\_0~X1~np\_\_1))~(\\
k21\_polyform~X0~X1))~(k11\_ranknull~k2\_bspace~(k17\_polyform~X0~\\
X1)~(k17\_polyform~X0~(k6\_xcmplx\_0~X1~np\_\_1))~(k21\_polyform~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
