\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{t25\_int\_4 (TMXUF11Ji9C1BdTnHWDjRQjkL766hRqqC7H)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_int\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_int\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{{r1\_int\_2}~{np\_\_1}}~{X0}})}}}\label{hyp:ehjdpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_nat\_d~X0~X1){\unicdbdjdcd}(r1\_nat\_d~X0~(k3\_xcmplx\_0~\\
X1~X2)))))\end{array}
\label{hyp:ehjdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v1\_xboole\_0~X0){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(v1\_xboole\_0~\\
X1))\end{array}
\label{hyp:ehidpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~X1~X2){\unicdbdjdcd}(r1\_nat\_d~(k1\_newton~X0~\\
X1)~(k1\_newton~X0~X2)))))\end{array}
\label{hyp:ehidjdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh (\preoh (X0=k6\_numbers){\unicdcdcdhd}(X1{\unicdcdgdad}k6\_numbers)){\unicdcdcdhd}(k1\_newton~X0~X1=k6\_numbers)){\unicdcdcdhd}\\
(\preoh (k1\_newton~X0~X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((X0=k6\_numbers){\unicdcdcdhd}(X1{\unicdcdgdad}k6\_numbers)))))\end{array}
\label{hyp:ehidhdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_nat\_d~X1~X0){\unicdbdjdcd}((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdid}(r1\_xxreal\_0~X1~\\
X0))))\end{array}
\label{hyp:ehhdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((r1\_nat\_d~X0~k6\_numbers){\unicdcdcdhd}(r1\_nat\_d~\\
np\_\_1~X0))\end{array}
\label{hyp:ehgdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k3\_xcmplx\_0~\\
X0~X0))\end{array}
\label{hyp:ehgdddpfihchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_newton}~{X0}}~{np\_\_1}}={X0}})}}}\label{hyp:ehfdpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_newton}~{X0}}~{k6\_numbers}}={np\_\_1}})}}}\label{hyp:ehedpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k6\_xcmplx\_0}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehedpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in X1){\unicdbdjded}(\preoh r1\_xxreal\_0~X1~X0)))\end{array}
\label{hyp:ehededpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(\preoh (k6\_numbers{\unicdcdgdad}X0){\unicdcdcdhd}(r1\_xxreal\_0~\\
X0~k6\_numbers))\end{array}
\label{hyp:ehddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh r1\_xxreal\_0~(k2\_xcmplx\_0~X0~X1)~X0){\unicdbdjded}(r1\_xxreal\_0~np\_\_1~X1)))\end{array}
\label{hyp:ehbdjdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_int\_1~X2){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh r1\_int\_1~(k3\_int\_2~X1~X0)~\\
X2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (v1\_int\_1~X3){\unicdcdcdhd}(k6\_int\_1~(k6\_xcmplx\_0~(k3\_xcmplx\_0~\\
X1~X3)~X2)~X0=k6\_numbers))))))\end{array}
\label{hyp:ehbdhdpfjgogehpfed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{{r1\_nat\_d}~{X0}}~{np\_\_1}})}{\unicdbdjdcd}{({{X0}={np\_\_1}})}})}}}\label{hyp:ehbdfdpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((r1\_nat\_d~X0~(k3\_xcmplx\_0~X1~X2)){\unicdcdcdhd}(r1\_int\_2~\\
X1~X0)){\unicdbdjdcd}(r1\_nat\_d~X0~X2))))\end{array}
\label{hyp:ehbdddpffgfhmgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~X0~(k2\_xcmplx\_0~\\
X1~X2)))))\end{array}
\label{hyp:ehbdcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(X1{\unicdcdgdad}k2\_xcmplx\_0~\\
X0~X2))))\end{array}
\label{hyp:ehbdadpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}((r1\_int\_2~\\
X0~X1){\unicdbdjdcd}(r1\_int\_2~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{np\_\_1}}~{np\_\_1}}={np\_\_1}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfchbdpfchbdpfchbd}
\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~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfogbgehpfeg}
\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}
{{\unicdcdaddd} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:chdgfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{v1\_xboole\_0}~{X0}}}\label{hyp:chdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(((r1\_xxreal\_0~\\
X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:mgfdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k2\_xcmplx\_0~X0~X1)~X2){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~X2){\unicdcdcdhd}(r1\_xxreal\_0~X1~X2)))))\end{array}
\label{hyp:mgcdedpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_int\_1~X1~X0){\unicdbdjdcd}((r1\_xxreal\_0~X0~k6\_numbers){\unicdcdcdid}(r1\_xxreal\_0~X1~\\
X0))))\end{array}
\label{hyp:mgbdedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{({{{k6\_xcmplx\_0}~{X0}}~{X0}})}})}}}\label{hyp:ggdgfdpfchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgedpfogfghhehpgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgcdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgbdpfhhdhjgfgchahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdcdcdhd}\\
(v7\_ordinal1~X1)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k1\_newton~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_int\_1~X0){\unicdcdcdhd}(v1\_int\_1~X1)){\unicdbdjdcd}(v1\_int\_1~\\
(k6\_int\_1~X0~X1))\end{array}
\label{hyp:egehpflggdpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((X2=k3\_int\_2~X0~X1){\unicdbdjded}((r1\_nat\_d~X2~X0){\unicdcdcdhd}((r1\_nat\_d~\\
X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(((r1\_nat\_d~X3~X0){\unicdcdcdhd}(r1\_nat\_d~\\
X3~X1)){\unicdbdjdcd}(r1\_nat\_d~X3~X2))))))))\end{array}
\label{hyp:egfdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_int\_2~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~\\
np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (r1\_int\_1~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}\\
np\_\_1){\unicdcdcdhd}(X1{\unicdcdgdad}X0))))))\end{array}
\label{hyp:egedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}((r1\_int\_2~\\
X0~X1){\unicdbdjded}(k3\_int\_2~X0~X1=np\_\_1)))\end{array}
\label{hyp:egddpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_int\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_int\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((X2=k3\_int\_2~X0~X1){\unicdbdjded}((r1\_int\_1~X2~X0){\unicdcdcdhd}((r1\_int\_1~\\
X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(((r1\_int\_1~X3~X0){\unicdcdcdhd}(r1\_int\_1~\\
X3~X1)){\unicdbdjdcd}(r1\_int\_1~X3~X2))))))))\end{array}
\label{hyp:egcdpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdghdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_int\_1}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgddpfjgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_int\_1}~{X0}})}}}\label{hyp:dgdgcdpfjgogehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfjgogehpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((v1\_int\_2~X1){\unicdcdcdhd}(r1\_int\_2~X1~X2)){\unicdbdjdcd}((r1\_xxreal\_0~\\
X0~k6\_numbers){\unicdcdcdid}({\unicdcdadad} X3 .  (v1\_int\_1~X3){\unicdbdjdcd}(k6\_int\_1~(k6\_xcmplx\_0~\\
(k3\_xcmplx\_0~X1~X3)~X2)~(k1\_newton~X1~X0){\unicdcdgdad}k6\_numbers))))))\end{array}$$
\end{theorem}
\end{document}
