\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{t45\_rvsum\_2 (TMbw6rBUH1xucb6joFdG2ezK96sgDTei6PC)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k19\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\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\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_valued\_0~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}(k19\_rvsum\_1~(k7\_finseq\_1~\\
X0~X1)=k5\_binop\_2~(k19\_rvsum\_1~X0)~(k19\_rvsum\_1~X1)))\end{array}
\label{hyp:ehjdhdpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
k2\_finseq\_2~(k2\_xcmplx\_0~X0~X1)~X2=k7\_finseq\_1~(k2\_finseq\_2~X0~\\
X2)~(k2\_finseq\_2~X1~X2)))\end{array}
\label{hyp:ehbdcdddpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
k23\_binop\_2~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdddpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
(v1\_relat\_1~(k2\_finseq\_2~X1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_finseq\_2~X1~\\
X0)){\unicdcdcdhd}((v1\_finseq\_1~(k2\_finseq\_2~X1~X0)){\unicdcdcdhd}(v1\_valued\_0~(k2\_finseq\_2~\\
X1~X0)))))\end{array}
\label{hyp:ggdgbdpfogfghhehpgog}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfchghdhfhngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}(k19\_rvsum\_1~(k2\_finseq\_2~(k23\_binop\_2~X0~X1)~\\
X2)=k5\_binop\_2~(k19\_rvsum\_1~(k2\_finseq\_2~X0~X2))~(k19\_rvsum\_1~\\
(k2\_finseq\_2~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
