\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{t18\_vectsp11 (TMTfwkP1cmfS3WprXNyVrgFoynGwGQXYkSi)}
\maketitle
Let $ l1\_struct\_0 : {{\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 $ 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 $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_vectsp11 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_group\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_partfun1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k12\_monoid\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}(k3\_group\_4~X0~(k6\_finseq\_1~(u1\_struct\_0~X0))=k1\_group\_1~\\
X0)\end{array}
\label{hyp:ehidpfhgchpgfhahpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k4\_binop\_1~(u1\_struct\_0~(k15\_monoid\_0~X0))~(u2\_algstr\_0~\\
(k15\_monoid\_0~X0))=k6\_partfun1~X0\end{array}
\label{hyp:ehhdfdpfngpgogpgjgegpfad}
\end{equation}
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 v2\_struct\_0~X0){\unicdcdcdhd}((v1\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}(k4\_binop\_1~(u1\_struct\_0~X0)~(u2\_algstr\_0~X0)=k1\_group\_1~\\
X0)\end{array}
\label{hyp:ehcdcdpfhgchpgfhahpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v7\_ordinal1~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k5\_finseq\_2~X0~X1~X2=k2\_finseq\_2~X1~\\
X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_relat\_1~(k2\_finseq\_2~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k2\_finseq\_2~X0~X1)){\unicdcdcdhd}((v3\_card\_1~(k2\_finseq\_2~\\
X0~X1)~X0){\unicdcdcdhd}(v1\_finseq\_1~(k2\_finseq\_2~X0~X1)))))\end{array}
\label{hyp:ggdgedpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v2\_struct\_0~(k15\_monoid\_0~X0)){\unicdcdcdhd}((v15\_algstr\_0~\\
(k15\_monoid\_0~X0)){\unicdcdcdhd}(v1\_group\_1~(k15\_monoid\_0~X0)))\end{array}
\label{hyp:ggdgddpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_monoid\_0~X1~X0){\unicdbdjdcd}\\
(l3\_algstr\_0~X1))\end{array}
\label{hyp:egehpfngcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgddpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k3\_struct\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k3\_struct\_0~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~(k3\_struct\_0~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v15\_algstr\_0~(k15\_monoid\_0~X0)){\unicdcdcdhd}(m2\_monoid\_0~(k15\_monoid\_0~\\
X0)~(k12\_monoid\_0~X0))\end{array}
\label{hyp:egehpflgbdfdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v15\_algstr\_0~(k12\_monoid\_0~X0)){\unicdcdcdhd}((v1\_monoid\_0~(\\
k12\_monoid\_0~X0)){\unicdcdcdhd}(l3\_algstr\_0~(k12\_monoid\_0~X0)))\end{array}
\label{hyp:egehpflgbdcdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k6\_finseq\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:eggdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}(\\
(v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((X3=k1\_vectsp11~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k15\_monoid\_0~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X4=X1){\unicdbdjdcd}(X3=k3\_group\_4~\\
(k15\_monoid\_0~(u1\_struct\_0~X0))~(k5\_finseq\_2~(u1\_struct\_0~(k15\_monoid\_0~\\
(u1\_struct\_0~X0)))~X2~X4))))))))\end{array}
\label{hyp:egedpfghfgdgehdhahbdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}(k3\_struct\_0~X0=k6\_partfun1~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egedpfdhehchfhdgehpfad}
\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 .  {{({{{v3\_card\_1}~{X0}}~{k1\_xboole\_0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{X0}})}}}\label{hyp:dgdghdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfghfgdgehdhahbdbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k1\_vectsp11~X0~\\
X1~k1\_xboole\_0)~(k3\_struct\_0~X0)))\end{array}$$
\end{theorem}
\end{document}
