From d72200d0c3e2e8ea026aac5909b3e57bff5d997c Mon Sep 17 00:00:00 2001 From: Ralf Jung <jung@mpi-sws.org> Date: Thu, 10 Mar 2016 10:15:18 +0100 Subject: [PATCH] rant about division... --- docs/algebra.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/algebra.tex b/docs/algebra.tex index 18f3e71dd..568a937c3 100644 --- a/docs/algebra.tex +++ b/docs/algebra.tex @@ -84,7 +84,7 @@ For every $n$, we obtain a proof that $\melt \mincl{n} \meltB$. From this, we could extract a sequence of witnesses $(\meltC_m)_{m}$, and we need to arrive at a single witness $\meltC$ showing that $\melt \leq \meltB$. Without the division operator, there is no reason to believe that such a witness exists. However, since we can use the division operator, and since we know that this operator is \emph{non-expansive}, we can pick $\meltC \eqdef \meltB \mdiv \melt$, and then we can prove that this is indeed the desired witness. -\ralf{Do we actually need this property anywhere?} +\ralf{The only reason we actually have division is that we are working constructively \emph{and}, at the same time, remain compatible with a classic interpretation of the existential. This is pretty silly.} \paragraph{The extension axiom (\ruleref{cmra-extend}).} Notice that the existential quantification in this axiom is \emph{constructive}, \ie it is a sigma type in Coq. -- GitLab