\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{t75\_fvsum\_1 (TMSpZayEf3G6woPFxd4DrnCf2tWi3WVNWtG)}
\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 $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_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 $ k5\_fvsum\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_algstr\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_finsop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_finseqop : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_algstr\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~\\
X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))){\unicdbdjdcd}(v1\_setwiseo~(u1\_algstr\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:ehidpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~X0){\unicdbdjdcd}(((v1\_binop\_1~X1~X0){\unicdcdcdhd}((v2\_binop\_1~X1~X0){\unicdcdcdhd}((v1\_setwiseo~\\
X1~X0){\unicdcdcdhd}(v1\_finseqop~X1~X0)))){\unicdbdjdcd}(k3\_funct\_2~X0~X0~(k5\_finseqop~X0~\\
X1)~(k1\_finsop\_1~X0~X2~X1)=k1\_finsop\_1~X0~(k4\_finseqop~X0~X0~X2~(\\
k5\_finseqop~X0~X1))~X1))))\end{array}
\label{hyp:ehddbdpfdhfgehhhpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v1\_algstr\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))){\unicdbdjdcd}\\
(r2\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~(k5\_finseqop~(u1\_struct\_0~\\
X0)~(u1\_algstr\_0~X0))~(k5\_vectsp\_1~X0))\end{array}
\label{hyp:ehbdfdpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v1\_algstr\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))){\unicdbdjdcd}\\
(v1\_finseqop~(u1\_algstr\_0~X0)~(u1\_struct\_0~X0))\end{array}
\label{hyp:ehbdedpfggghdhfhngpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\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 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_0~X0)){\unicdcdcdhd}((v1\_funct\_2~(u1\_algstr\_0~\\
X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(v2\_binop\_1~(u1\_algstr\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ggdgcdpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~\\
X0))){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_0~X0)){\unicdcdcdhd}((v1\_funct\_2~(u1\_algstr\_0~\\
X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(v1\_binop\_1~(u1\_algstr\_0~X0)~(u1\_struct\_0~X0))))\end{array}
\label{hyp:ggdgbdpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_algstr\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_algstr\_0~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k5\_vectsp\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k5\_vectsp\_1~X0)~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(k5\_vectsp\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflgfdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(u1\_struct\_0~X0))){\unicdbdjdcd}(m2\_finseq\_1~(k5\_fvsum\_1~\\
X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgfdpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_finseqop~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k5\_finseqop~X0~X1)~X0~X0){\unicdcdcdhd}(m1\_subset\_1~(\\
k5\_finseqop~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))))\end{array}
\label{hyp:egehpflgfdpfggjgogdhfgbhpgah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_finseq\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_finsop\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgbdpfggjgogdhpgahpfbd}
\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}(l2\_algstr\_0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k4\_rlvect\_1~X0~\\
X1=k1\_finsop\_1~(u1\_struct\_0~X0)~X1~(u1\_algstr\_0~X0)))\end{array}
\label{hyp:egidpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k5\_fvsum\_1~X0~X1=k4\_finseqop~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~(k5\_vectsp\_1~X0)))\end{array}
\label{hyp:egedpfggghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_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}((X1=k5\_vectsp\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X0)~X1~X2=k4\_algstr\_0~X0~X2))))\end{array}
\label{hyp:egbdddpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}(v4\_rlvect\_1~X0))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v1\_algstr\_1~X0)))\end{array}
\label{hyp:dgdgbdpfggghdhfhngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdfdpfggghdhfhngpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k4\_rlvect\_1~X0~\\
(k5\_fvsum\_1~X0~X1)=k4\_algstr\_0~X0~(k4\_rlvect\_1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
