equal
deleted
inserted
replaced
2983 qed |
2983 qed |
2984 |
2984 |
2985 declare Sup_set_fold [where 'a = "'a set", code] |
2985 declare Sup_set_fold [where 'a = "'a set", code] |
2986 |
2986 |
2987 lemma (in complete_lattice) INF_set_fold: |
2987 lemma (in complete_lattice) INF_set_fold: |
2988 "INFIMUM (set xs) f = fold (inf \<circ> f) xs top" |
2988 "\<Sqinter>(f ` set xs) = fold (inf \<circ> f) xs top" |
2989 using Inf_set_fold [of "map f xs"] by (simp add: fold_map) |
2989 using Inf_set_fold [of "map f xs"] by (simp add: fold_map) |
2990 |
2990 |
2991 lemma (in complete_lattice) SUP_set_fold: |
2991 lemma (in complete_lattice) SUP_set_fold: |
2992 "SUPREMUM (set xs) f = fold (sup \<circ> f) xs bot" |
2992 "\<Squnion>(f ` set xs) = fold (sup \<circ> f) xs bot" |
2993 using Sup_set_fold [of "map f xs"] by (simp add: fold_map) |
2993 using Sup_set_fold [of "map f xs"] by (simp add: fold_map) |
2994 |
2994 |
2995 |
2995 |
2996 subsubsection \<open>Fold variants: @{const foldr} and @{const foldl}\<close> |
2996 subsubsection \<open>Fold variants: @{const foldr} and @{const foldl}\<close> |
2997 |
2997 |