X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=lemmas.tex;h=aeb656479c497363460d14de95af921d326ccd58;hp=577f5135c408bf081ccea472f6e02fa9779cd6a2;hb=57f83cd8bc6bcf23e45739c00c83c9a8672ae701;hpb=7dc335c17ae313c006e2283a35ca214b213ffcd9;ds=sidebyside diff --git a/lemmas.tex b/lemmas.tex index 577f513..aeb6564 100644 --- a/lemmas.tex +++ b/lemmas.tex @@ -56,14 +56,16 @@ So by Base Acyclic $D \isin B \implies D \notin \py$. \subsection{Tip Self Inpatch} Given Exclusive Tip Contents and Base Acyclic for $C$, $$ - \bigforall_{C \in \py} C \haspatch \p + \bigforall_{C \in \py} C \haspatch \p \land \neg[ C \nothaspatch \p ] $$ Ie, tip commits contain their own patch. \proof{ Apply Exclusive Tip Contents to some $D \in \py$: $ \bigforall_{C \in \py}\bigforall_{D \in \py} - D \isin C \equiv D \le C $ + D \isin C \equiv D \le C $. +Thus $C \haspatch \p$. +And, since $C \le C$, $C \isin C$. Therefore $\neg[ C \nothaspatch \p ]$ } \subsection{Exact Ancestors}