diff options
Diffstat (limited to 'spartan/data/List.thy')
| -rw-r--r-- | spartan/data/List.thy | 20 |
1 files changed, 15 insertions, 5 deletions
diff --git a/spartan/data/List.thy b/spartan/data/List.thy index 52f042b..c581019 100644 --- a/spartan/data/List.thy +++ b/spartan/data/List.thy @@ -50,19 +50,29 @@ lemmas abbreviation "ListRec A C \<equiv> ListInd A (\<lambda>_. C)" +Lemma (derive) ListCase: + assumes + "A: U i" "\<And>xs. xs: List A \<Longrightarrow> C xs: U i" and + nil_case: "c\<^sub>0: C (nil A)" and + cons_case: "\<And>x xs. \<lbrakk>x: A; xs: List A\<rbrakk> \<Longrightarrow> f x xs: C (cons A x xs)" and + "xs: List A" + shows "?List_cases A (\<lambda>xs. C xs) c\<^sub>0 (\<lambda>x xs. f x xs) xs: C xs" + by (elim xs) (fact nil_case, rule cons_case) + +lemmas List_cases [cases] = ListCase[rotated 4] + + +section \<open>Notation\<close> + definition nil_i ("[]") where [implicit]: "[] \<equiv> nil ?" -definition cons_i (infixr "#" 50) +definition cons_i (infixr "#" 120) where [implicit]: "x # xs \<equiv> cons ? x xs" translations "[]" \<leftharpoondown> "CONST List.nil A" "x # xs" \<leftharpoondown> "CONST List.cons A x xs" - - -section \<open>List notation\<close> - syntax "_list" :: \<open>args \<Rightarrow> o\<close> ("[_]") translations |