\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{t19\_clvect\_1 (TMYgxgGJjVn51nSvM2M3J8eDiS2ToTKustC)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_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 $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\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 $ k4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k4\_rlvect\_1~\\
X0~(k3\_finseq\_4~(u1\_struct\_0~X0)~X1~X2~X3)=k1\_algstr\_0~X0~(k4\_rlvect\_1~\\
X0~(k2\_finseq\_4~(u1\_struct\_0~X0)~X1~X2))~X3))))\end{array}
\label{hyp:ehgdedpfchmgghfgdgehpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}(l1\_clvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k4\_rlvect\_1~X0~(k2\_finseq\_4~(u1\_struct\_0~X0)~X1~X1)=k1\_clvect\_1~\\
X0~X1~(k8\_complex1~k6\_complex1~k6\_complex1)))\end{array}
\label{hyp:ehbdhdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{np\_\_1}}={np\_\_2}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchbdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k2\_numbers)){\unicdbdjdcd}(k8\_complex1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}((v5\_clvect\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_clvect\_1~\\
X0~X1~k6\_complex1=X1)))\end{array}
\label{hyp:egfdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_complex1}={np\_\_1}}\label{hyp:egedpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}((v3\_clvect\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_clvect\_1~X0~\\
X3~(k2\_xcmplx\_0~X1~X2)=k1\_algstr\_0~X0~(k1\_clvect\_1~X0~X3~X1)~(k1\_clvect\_1~\\
X0~X3~X2))))))\end{array}
\label{hyp:egddpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_numbers}})}}}\label{hyp:egcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfdgmgghfgdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}(l1\_clvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k4\_rlvect\_1~X0~(k3\_finseq\_4~(u1\_struct\_0~X0)~X1~X1~X1)=k1\_clvect\_1~\\
X0~X1~(k8\_complex1~(k8\_complex1~k6\_complex1~k6\_complex1)~k6\_complex1)))\end{array}$$
\end{theorem}
\end{document}
