\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{t36\_afproj (TMXRNjK7uNC1P6Ueni3hnN1ujMXjRo7mdYL)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_afproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_afproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ g1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k12\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((r1\_aff\_4~X0~X1~X2){\unicdcdcdhd}(r1\_aff\_4~X0~X2~X3)){\unicdbdjdcd}((X2=k1\_xboole\_0){\unicdcdcdid}\\
(r1\_aff\_4~X0~X1~X3))))))\end{array}
\label{hyp:ehgdadpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(\preoh (v1\_aff\_4~X1~X0){\unicdcdcdhd}(X1=k1\_xboole\_0)))\end{array}
\label{hyp:ehfdjdpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((r5\_aff\_1~X0~X1~X2){\unicdcdcdhd}(r1\_aff\_4~X0~X2~X3)){\unicdbdjdcd}(r1\_aff\_4~X0~X1~X3)))))\end{array}
\label{hyp:ehfdgdpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_4~X1~X0){\unicdcdcdhd}(v1\_aff\_4~X2~X0)){\unicdbdjdcd}((k6\_afproj~X0~X1=k6\_afproj~\\
X0~X2){\unicdbdjded}(r1\_aff\_4~X0~X1~X2)))))\end{array}
\label{hyp:ehbdddpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)){\unicdbdjdcd}((k5\_afproj~X0~X1=k5\_afproj~\\
X0~X2){\unicdbdjded}(r5\_aff\_1~X0~X1~X2)))))\end{array}
\label{hyp:ehbdbdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X3~X1)))){\unicdbdjdcd}\\
(k1\_domain\_1~X0~X1~X2~X3=k4\_tarski~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  {\unicdcdadad} X5 .  (g1\_incsp\_1~X0~X1~X2=g1\_incsp\_1~X3~X4~X5){\unicdbdjdcd}\\
((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(m1\_subset\_1~(u3\_incsp\_1~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0))))\end{array}
\label{hyp:egehpffhddpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{u2\_incsp\_1}~{X0}})}}}})}}}\label{hyp:egehpffhcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_incsp\_1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{u1\_incsp\_1}~{X0}})}}}})}}}\label{hyp:egehpffhbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
((v1\_incsp\_1~(k14\_afproj~X0)){\unicdcdcdhd}(l1\_incsp\_1~(k14\_afproj~X0)))\end{array}
\label{hyp:egehpflgbdedpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
(m1\_subset\_1~(k12\_afproj~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_afproj~\\
X0)~(k8\_afproj~X0))))\end{array}
\label{hyp:egehpflgbdcdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}((r1\_incsp\_1~\\
X0~X1~X2){\unicdbdjded}(k1\_domain\_1~(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~X1~X2 \in u3\_incsp\_1~\\
X0))))\end{array}
\label{hyp:egbdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
(k14\_afproj~X0=g1\_incsp\_1~(k7\_afproj~X0)~(k8\_afproj~X0)~(k12\_afproj~\\
X0))\end{array}
\label{hyp:egbdedpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_afproj~\\
X0)~(k8\_afproj~X0)))){\unicdbdjdcd}((X1=k12\_afproj~X0){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
(k4\_tarski~X2~X3 \in X1){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}((X2=k5\_afproj~X0~X4){\unicdcdcdhd}((X3=k6\_afproj~X0~X5){\unicdcdcdhd}\\
((v1\_aff\_1~X4~X0){\unicdcdcdhd}((v1\_aff\_4~X5~X0){\unicdcdcdhd}(r1\_aff\_4~X0~X4~X5))))))))))\end{array}
\label{hyp:egbdcdpfbgggahchpgkg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}((v1\_incsp\_1~X0){\unicdbdjdcd}(X0=g1\_incsp\_1~\\
(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~(u3\_incsp\_1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u2\_incsp\_1~(k14\_afproj~X0))){\unicdbdjdcd}(((X3=k5\_afproj~\\
X0~X1){\unicdcdcdhd}((X4=k6\_afproj~X0~X2){\unicdcdcdhd}((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_4~X2~X0)))){\unicdbdjdcd}\\
((r1\_incsp\_1~(k14\_afproj~X0)~X3~X4){\unicdbdjded}(r1\_aff\_4~X0~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
