# HG changeset patch # User desharna # Date 1654672797 -7200 # Node ID 47abacd97f7b58cd97ebd516723d21840bfc1b15 # Parent 2e8a2dc7a1e6369865389ea721b5f102aec73aa0# Parent a4fa039a6a60bf7ae39606178da1a9c9ad2ea421 merged diff -r 2e8a2dc7a1e6 -r 47abacd97f7b NEWS --- a/NEWS Wed Jun 08 09:12:51 2022 +0200 +++ b/NEWS Wed Jun 08 09:19:57 2022 +0200 @@ -54,6 +54,7 @@ reflp_onI reflp_on_Inf reflp_on_Sup + reflp_on_empty[simp] reflp_on_inf reflp_on_mono reflp_on_subset @@ -63,7 +64,9 @@ totalpI totalp_onD totalp_onI + totalp_on_empty[simp] totalp_on_subset + totalp_on_total_on_eq[pred_set_conv] * Theory "HOL-Library.Multiset": - Consolidated operation and fact names. diff -r 2e8a2dc7a1e6 -r 47abacd97f7b src/HOL/Relation.thy --- a/src/HOL/Relation.thy Wed Jun 08 09:12:51 2022 +0200 +++ b/src/HOL/Relation.thy Wed Jun 08 09:19:57 2022 +0200 @@ -236,6 +236,9 @@ lemma refl_on_empty [simp]: "refl_on {} {}" by (simp add: refl_on_def) +lemma reflp_on_empty [simp]: "reflp_on {} R" + by (auto intro: reflp_onI) + lemma refl_on_singleton [simp]: "refl_on {x} {(x, x)}" by (blast intro: refl_onI) @@ -525,6 +528,9 @@ abbreviation totalp where "totalp \ totalp_on UNIV" +lemma totalp_on_refl_on_eq[pred_set_conv]: "totalp_on A (\x y. (x, y) \ r) \ total_on A r" + by (simp add: totalp_on_def total_on_def) + lemma totalp_onI: "(\x y. x \ A \ y \ A \ x \ y \ R x y \ R y x) \ totalp_on A R" by (simp add: totalp_on_def) @@ -548,6 +554,9 @@ lemma total_on_empty [simp]: "total_on {} r" by (simp add: total_on_def) +lemma totalp_on_empty [simp]: "totalp_on {} R" + by (auto intro: totalp_onI) + lemma total_on_singleton [simp]: "total_on {x} {(x, x)}" unfolding total_on_def by blast