From: Ian Jackson Date: Mon, 12 Mar 2012 18:04:51 +0000 (+0000) Subject: more clarifications and fixes from reread X-Git-Tag: f0.2~36 X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=commitdiff_plain;ds=sidebyside;h=e090a73b6d5a31fae5d7bc1244ea8defdeabae05;p=topbloke-formulae.git more clarifications and fixes from reread --- diff --git a/article.tex b/article.tex index 70cee81..4af8e05 100644 --- a/article.tex +++ b/article.tex @@ -676,7 +676,7 @@ Used for removing a branch dependency. R^+ \in \pry \land R^- = \baseof{R^+} }\] \[ \eqn{ Into Base }{ - L \in \pn + L \in \pqn }\] \[ \eqn{ Unique Tip }{ \pendsof{L}{\pry} = \{ R^+ \} @@ -696,7 +696,7 @@ is a descendant, not an ancestor, of the 2nd parent.) \subsection{No Replay} -By definition of $\merge$, +By $\merge$, $D \isin C \implies D \isin L \lor D \isin R^- \lor D = C$. So, by Ordering of Ingredients, Ingredients Prevent Replay applies. $\qed$ @@ -712,7 +712,8 @@ Trivially $D \isin C$. OK. \subsubsection{For $D \neq C, D \not\le L$:} -By No Replay $D \not\isin L$. Also $D \not\le R^-$ hence +By No Replay for $L$, $D \not\isin L$. +Also, by Ordering of Ingredients, $D \not\le R^-$ hence $D \not\isin R^-$. Thus $D \not\isin C$. OK. \subsubsection{For $D \neq C, D \le L, D \in \pry$:} @@ -723,7 +724,7 @@ By Tip Self Inpatch for $R^+$, $D \isin R^+ \equiv D \le R^+$, but by by Unique Tip, $D \le R^+ \equiv D \le L$. So $D \isin R^+$. -By Base Acyclic, $D \not\isin R^-$. +By Base Acyclic for $R^-$, $D \not\isin R^-$. Apply $\merge$: $D \not\isin C$. OK. @@ -737,7 +738,7 @@ $\qed$ \subsection{Unique Base} -Into Base means that $C \in \pn$, so Unique Base is not +Into Base means that $C \in \pqn$, so Unique Base is not applicable. $\qed$ \subsection{Tip Contents} @@ -746,11 +747,11 @@ Again, not applicable. $\qed$ \subsection{Base Acyclic} -By Base Acyclic for $L$, $D \isin L \implies D \not\in \py$. -And by Into Base $C \not\in \py$. +By Into Base and Base Acyclic for $L$, $D \isin L \implies D \not\in \pqy$. +And by Into Base $C \not\in \pqy$. Now from Desired Contents, above, $D \isin C \implies D \isin L \lor D = C$, which thus -$\implies D \not\in \py$. $\qed$. +$\implies D \not\in \pqy$. $\qed$. \subsection{Coherence and Patch Inclusion}