X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=merge.tex;h=48e72702c780d17648ffe6ef5d5e5a6b1253fcce;hp=94b38fe9648d88f2022ba9ee57aae96d35806a2e;hb=03a40d446bbe0d0a7f8d7c2e4628b7eea9be3eec;hpb=45d3a192063cc2e12dea5fc84a8ffcf7c2a220e2 diff --git a/merge.tex b/merge.tex index 94b38fe..48e7270 100644 --- a/merge.tex +++ b/merge.tex @@ -165,14 +165,15 @@ $D \isin Y \equiv D \le Y$. $D \not\isin X$. We will show for each of various cases that if $M \haspatch \p$, $D \not\isin C$, -whereas if $M \nothaspatch \p$, $D \isin C \equiv \land D \le C$. +whereas if $M \nothaspatch \p$, $D \isin C \equiv D \le C$. And by $Y \haspatch \p$, $\exists_{F \in \py} F \le Y$ and this $F \le C$ so this suffices. Consider $D = C$: Thus $C \in \py, L \in \py$. -By Tip Own Contents, $\neg[ L \nothaspatch \p ]$ so $L \neq X$, +By Tip Own Contents, $L \haspatch \p$ so $L \neq X$, therefore we must have $L=Y$, $R=X$. -By Tip Merge $M = \baseof{L}$ so $M \in \pn$ so +Conversely $R \not\in \py$ +so by Tip Merge $M = \baseof{L}$. Thus $M \in \pn$ so by Base Acyclic $M \nothaspatch \p$. By $\merge$, $D \isin C$, and $D \le C$. OK.