\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t79\_pnproc\_1 (TMRdp8bKF1dKWtK9ZF6H2DWhEAGaoZsf8Gt)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_pnproc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\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\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v2\_finseq\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v2\_finseq\_1~\\
X3))){\unicdbdjdcd}(\preoh (r1\_tarski~X2~X0){\unicdcdcdhd}((r1\_tarski~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v2\_finseq\_1~X4))){\unicdbdjdcd}(\preoh (X4=k2\_xboole\_0~\\
X2~(k12\_pnproc\_1~X3~(k3\_finseq\_1~X0))){\unicdcdcdhd}((k4\_finseq\_1~(k15\_finseq\_1~\\
X4)=k2\_finseq\_1~(k2\_nat\_1~(k3\_finseq\_1~(k15\_finseq\_1~X2))~(k3\_finseq\_1~\\
(k15\_finseq\_1~X3)))){\unicdcdcdhd}(k15\_finseq\_1~X4=k2\_xboole\_0~(k15\_finseq\_1~\\
X2)~(k12\_pnproc\_1~(k15\_finseq\_1~X3)~(k3\_finseq\_1~(k15\_finseq\_1~\\
X2))))))))))))\end{array}
\label{hyp:ehhdidpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}(k7\_finseq\_1~X0~X1=k2\_xboole\_0~X0~(k12\_pnproc\_1~X1~(k3\_finseq\_1~\\
X0))))\end{array}
\label{hyp:ehgdbdpfahogahchpgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v2\_finseq\_1~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k15\_finseq\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k15\_finseq\_1~\\
X0)){\unicdcdcdhd}(v1\_finseq\_1~(k15\_finseq\_1~X0))))\end{array}
\label{hyp:ggdgbdfdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdjdpfahogahchpgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v2\_finseq\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v2\_finseq\_1~\\
X3))){\unicdbdjdcd}(\preoh (r1\_tarski~X2~X0){\unicdcdcdhd}((r1\_tarski~X3~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  ((v1\_relat\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v2\_finseq\_1~X4))){\unicdbdjdcd}(\preoh (X4=k2\_xboole\_0~\\
X2~(k12\_pnproc\_1~X3~(k3\_finseq\_1~X0))){\unicdcdcdhd}(k7\_finseq\_1~(k15\_finseq\_1~\\
X2)~(k15\_finseq\_1~X3)=k15\_finseq\_1~X4))))))))\end{array}$$
\end{theorem}
\end{document}
