, \text{where} \{J,K\} = \{L,R\}
}\]
\[ \eqn{ Foreign Merges }{
- \patchof{L} = \bot \implies \patchof{R} = \bot
+ \isforeign{L} \implies \isforeign{R}
}\]
\subsection{Non-Topbloke merges}
-We require both $\patchof{L} = \bot$ and $\patchof{R} = \bot$
+We require both $\isforeign{L}$ and $\isforeign{R}$
(Foreign Merges, above).
I.e. not only is it forbidden to merge into a Topbloke-controlled
branch without Topbloke's assistance, it is also forbidden to
merge any Topbloke-controlled branch into any plain git branch.
Given those conditions, Tip Merge and Merge Acyclic do not apply.
-By Foreign Contents of $L$, $\patchof{M} = \bot$ as well.
+By Foreign Contents of $L$, $\isforeign{M}$ as well.
So by Foreign Contents for any $A \in \{L,M,R\}$,
$\forall_{\p, D \in \py} D \not\le A$
so $\pendsof{A}{\py} = \{ \}$ and the RHS of both Merge Ends
suitable.
For $L \not\in \py$, $\pancsof{C}{\py} = \pancsof{L}{\py} \cup
-\pancsof{R}{\py}$. So $T$ from Suitable Tip is a suitable $T$ for
+\pancsof{R}{\py}$. So $T$ from Suitable Tips is a suitable $T$ for
Unique Tips.
$\qed$
\subsection{Foreign Inclusion}
-Consider some $D$ s.t. $\patchof{D} = \bot$.
+Consider some $D \in \foreign$.
By Foreign Inclusion of $L, M, R$:
$D \isin L \equiv D \le L$;
$D \isin M \equiv D \le M$;
\subsection{Foreign Contents}
-Only relevant if $\patchof{L} = \bot$, in which case
-$\patchof{C} = \bot$ and by Foreign Merges $\patchof{R} = \bot$,
+Only relevant if $\isforeign{L}$, in which case
+$\isforeign{C}$ and by Foreign Merges $\isforeign{R}$,
so Totally Foreign Contents applies. $\qed$