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\begin{document}
\title{t115\_scmyciel (TMQRx8wcdbmozPGAprSZMTDv4YPD27SR3b7)}
\maketitle
Let $ v4\_scmyciel : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_scmyciel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k12\_scmyciel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v4\_scmyciel~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v4\_scmyciel~(k1\_funct\_1~(k13\_scmyciel~X0)~X1))\end{array}
\label{hyp:ggdgcdfdpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_scmyciel~X0){\unicdbdjdcd}((v1\_relat\_1~(k13\_scmyciel~X0)){\unicdcdcdhd}\\
((v4\_relat\_1~(k13\_scmyciel~X0)~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~(k13\_scmyciel~\\
X0)){\unicdcdcdhd}(v1\_partfun1~(k13\_scmyciel~X0)~k5\_numbers))))\end{array}
\label{hyp:egehpflgbdddpfdhdgngjhdgjgfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v4\_scmyciel~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~k5\_numbers)))){\unicdbdjdcd}\\
((X1=k13\_scmyciel~X0){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdcdcdhd}((X1=X2){\unicdcdcdhd}((k1\_funct\_1~X2~k6\_numbers=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (\\
v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v4\_scmyciel~X4){\unicdbdjdcd}((X4=k1\_funct\_1~\\
X2~X3){\unicdbdjdcd}(k1\_funct\_1~X2~(k1\_nat\_1~X3~np\_\_1)=k12\_scmyciel~X4)))))))))\end{array}
\label{hyp:egcdgdpfdhdgngjhdgjgfgmg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdfdpfdhdgngjhdgjgfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v4\_scmyciel~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v4\_scmyciel~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(k1\_funct\_1~(k13\_scmyciel~X0)~(k1\_nat\_1~X2~np\_\_1)=\\
k12\_scmyciel~(k1\_funct\_1~(k13\_scmyciel~X0)~X2))))\end{array}$$
\end{theorem}
\end{document}
