X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?p=topbloke-formulae.git;a=blobdiff_plain;f=merge.tex;h=fd45642df697518317032ed9c9956c62baf7c1dd;hp=f5038213bc5ce7b97b067cc00fcaa63d5ac0bd76;hb=57f83cd8bc6bcf23e45739c00c83c9a8672ae701;hpb=670d1b8cb1403203123ffd2d6c510f82bb7a335c diff --git a/merge.tex b/merge.tex index f503821..fd45642 100644 --- a/merge.tex +++ b/merge.tex @@ -233,14 +233,16 @@ By Tip Contents $D \isin L \equiv D \isin \baseof{L}$ and $D \isin R \equiv D \isin \baseof{R}$. +Apply Tip Merge condition. If $\baseof{L} = M$, trivially $D \isin M \equiv D \isin \baseof{L}.$ Whereas if $\baseof{L} = \baseof{M}$, by definition of $\base$, $\patchof{M} = \patchof{L} = \py$, so by Tip Contents of $M$, $D \isin M \equiv D \isin \baseof{M} \equiv D \isin \baseof{L}$. -So $D \isin M \equiv D \isin L$ and by $\merge$, +So $D \isin M \equiv D \isin L$ so by $\merge$, $D \isin C \equiv D \isin R$. But from Unique Base, -$\baseof{C} = R$ so $D \isin C \equiv D \isin \baseof{C}$. OK. +$\baseof{C} = \baseof{R}$. +Therefore $D \isin C \equiv D \isin \baseof{C}$. OK. $\qed$