From d27936801b2997af16814e2879c8bdf6f4eb7bcc Mon Sep 17 00:00:00 2001 From: Cyril Cohen Date: Mon, 18 Nov 2019 18:22:20 +0100 Subject: Adding `inj_compr` lemma in ssrfun. --- plugins/ssr/ssrfun.v | 3 +++ 1 file changed, 3 insertions(+) (limited to 'plugins') diff --git a/plugins/ssr/ssrfun.v b/plugins/ssr/ssrfun.v index b8affba541..dd847169b9 100644 --- a/plugins/ssr/ssrfun.v +++ b/plugins/ssr/ssrfun.v @@ -675,6 +675,9 @@ Proof. by move=> fK injf' x; apply: injf'. Qed. Lemma inj_comp : injective f -> injective h -> injective (f \o h). Proof. by move=> injf injh x y /injf; apply: injh. Qed. +Lemma inj_compr : injective (f \o h) -> injective h. +Proof. by move=> injfh x y /(congr1 f) /injfh. Qed. + Lemma can_comp f' h' : cancel f f' -> cancel h h' -> cancel (f \o h) (h' \o f'). Proof. by move=> fK hK x; rewrite /= fK hK. Qed. -- cgit v1.2.3