From b560d40113ecbf454ccf22c2bec820786a0ea11b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Violeta=20Hern=C3=A1ndez?= Date: Fri, 15 Jul 2022 20:48:42 +0000 Subject: [PATCH] feat(data/sum/basic): `sum.lift_rel` is a subrelation of `sum.lex` (#15358) Also trivial spacing fix. --- src/data/sum/basic.lean | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/data/sum/basic.lean b/src/data/sum/basic.lean index 97240afc4bd21..590a4957cca64 100644 --- a/src/data/sum/basic.lean +++ b/src/data/sum/basic.lean @@ -286,6 +286,8 @@ instance [decidable_rel r] [decidable_rel s] : decidable_rel (lex r s) protected lemma lift_rel.lex {a b : α ⊕ β} (h : lift_rel r s a b) : lex r s a b := by { cases h, exacts [lex.inl ‹_›, lex.inr ‹_›] } +lemma lift_rel_subrelation_lex : subrelation (lift_rel r s) (lex r s) := λ a b, lift_rel.lex + lemma lex.mono (hr : ∀ a b, r₁ a b → r₂ a b) (hs : ∀ a b, s₁ a b → s₂ a b) (h : lex r₁ s₁ x y) : lex r₂ s₂ x y := by { cases h, exacts [lex.inl (hr _ _ ‹_›), lex.inr (hs _ _ ‹_›), lex.sep _ _] } @@ -293,7 +295,7 @@ by { cases h, exacts [lex.inl (hr _ _ ‹_›), lex.inr (hs _ _ ‹_›), lex.se lemma lex.mono_left (hr : ∀ a b, r₁ a b → r₂ a b) (h : lex r₁ s x y) : lex r₂ s x y := h.mono hr $ λ _ _, id -lemma lex.mono_right (hs : ∀ a b, s₁ a b → s₂ a b) (h : lex r s₁ x y) : lex r s₂ x y := +lemma lex.mono_right (hs : ∀ a b, s₁ a b → s₂ a b) (h : lex r s₁ x y) : lex r s₂ x y := h.mono (λ _ _, id) hs lemma lex_acc_inl {a} (aca : acc r a) : acc (lex r s) (inl a) :=