\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{t23\_groupp\_1 (TMGpjk863FYnAJ4swEugFnmtiuYdbLL3GMz)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_group\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_group\_10 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_groupp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_group\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_groupp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(\preoh (r1\_int\_1~X1~(k1\_newton~X0~\\
X2)){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (X1=k1\_newton~X0~X3){\unicdcdcdhd}(r1\_xxreal\_0~\\
X3~X2))))))\end{array}
\label{hyp:ehcdpfhgchpgfhahahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~\\
X1~X0){\unicdbdjdcd}(r1\_nat\_d~(k7\_group\_1~X1)~(k7\_group\_1~X0)))\end{array}
\label{hyp:ehbdedidpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_nat\_d~X0~X1){\unicdbdjded}(r1\_int\_1~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(k7\_group\_1~\\
X0=k7\_struct\_0~X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdcdcdhd}((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))))){\unicdbdjdcd}(k2\_groupp\_1~X0~X1=k1\_groupp\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfhgchpgfhahahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}((v7\_ordinal1~\\
(k7\_struct\_0~X0)){\unicdcdcdhd}(v1\_card\_1~(k7\_struct\_0~X0)))\end{array}
\label{hyp:ggdgbdhdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1))))\end{array}
\label{hyp:egehpfngbdpfhgchpgfhahpfcd}
\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 .  {\unicdcdadad} X1 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdcdcdhd}((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))))){\unicdbdjdcd}(v7\_ordinal1~(k1\_groupp\_1~X0~X1))\end{array}
\label{hyp:egehpflgbdpfhgchpgfhahahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1)))){\unicdbdjdcd}((v2\_group\_10~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((\\
X2=k1\_groupp\_1~X0~X1){\unicdbdjded}(k7\_struct\_0~X1=k1\_newton~X0~X2)))))\end{array}
\label{hyp:egcdpfhgchpgfhahahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v8\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~\\
X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~\\
X1~X0){\unicdbdjdcd}(v8\_struct\_0~X1))\end{array}
\label{hyp:dgdgddpfhgchpgfhahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdcdcdhd}((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v8\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}((v2\_group\_10~X1~X0){\unicdcdcdhd}(l3\_algstr\_0~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_group\_2~X2~X1){\unicdbdjdcd}(v2\_group\_10~X2~X0))\end{array}
\label{hyp:dgdgcdpfhgchpgfhahahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_group\_2~X1~X0){\unicdbdjdcd}(v3\_group\_1~\\
X1))\end{array}
\label{hyp:dgdgbdpfhgchpgfhahpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfhgchpgfhahahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v8\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}((v3\_group\_1~\\
X1){\unicdcdcdhd}(l3\_algstr\_0~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_group\_2~X2~X1){\unicdbdjdcd}((v2\_group\_10~\\
X1~X0){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_groupp\_1~X0~X2)~(k2\_groupp\_1~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
