merge any Topbloke-controlled branch into any plain git branch.
Given those conditions, Tip Merge and Merge Acyclic do not apply.
-And by Foreign Contents for (wlog) Y, $\forall_{\p, D \in \py} D \not\le Y$
-so then by No Replay $D \not\isin Y$
-so $\neg [ Y \haspatch \p ]$ so neither
-Merge Ends condition applies.
+By Foreign Contents of $L$, $\patchof{M} = \bot$ 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
+conditions are satisifed.
So a plain git merge of non-Topbloke branches meets the conditions and
is therefore consistent with our model.
\subsubsection{For $L \nothaspatch \p, R \nothaspatch \p$:}
$D \not\isin L \land D \not\isin R$. $C \not\in \py$ (otherwise $L
-\in \py$ ie $L \haspatch \p$ by Tip Self Inpatch for $L$). So $D \neq C$.
+\in \py$ ie $\neg[ L \nothaspatch \p ]$ by Tip Own Contents for $L$).
+So $D \neq C$.
Applying $\merge$ gives $D \not\isin C$ i.e. $C \nothaspatch \p$.
\subsubsection{For $L \haspatch \p, R \haspatch \p$:}
Recall that we are considering $D \in \py$.
$D \isin Y \equiv D \le Y$. $D \not\isin X$.
We will show for each of
-various cases that $D \isin C \equiv M \nothaspatch \p \land D \le C$
-(which suffices by definition of $\haspatch$ and $\nothaspatch$).
+various cases that
+if $M \haspatch \p$, $D \not\isin C$,
+whereas if $M \nothaspatch \p$, $D \isin C \equiv \land D \le C$.
-Consider $D = C$: Thus $C \in \py, L \in \py$. By Tip Contents
-for $L$, $L \isin L$ so $\neg [ L \nothaspatch \p ]$.
-Therefore we must have $L=Y$, $R=X$.
+Consider $D = C$: Thus $C \in \py, L \in \py$.
+By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$,
+therefore we must have $L=Y$, $R=X$.
By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so
by Base Acyclic $M \nothaspatch \p$. By $\merge$, $D \isin C$,
-and $D \le C$, consistent with $C \haspatch \p$. OK.
+and $D \le C$. OK.
Consider $D \neq C, M \nothaspatch \p, D \isin Y$:
$D \le Y$ so $D \le C$.
~ian / topbloke-formulae.git / blobdiff