diff options
Diffstat (limited to '')
| -rw-r--r-- | mltt/lib/List.thy | 10 | ||||
| -rw-r--r-- | mltt/lib/Maybe.thy | 2 | ||||
| -rw-r--r-- | mltt/lib/Prelude.thy | 2 |
3 files changed, 7 insertions, 7 deletions
diff --git a/mltt/lib/List.thy b/mltt/lib/List.thy index 4beb9b6..0cd43c8 100644 --- a/mltt/lib/List.thy +++ b/mltt/lib/List.thy @@ -83,7 +83,7 @@ section \<open>Standard functions\<close> subsection \<open>Head and tail\<close> -Definition head: +Lemma (def) head: assumes "A: U i" "xs: List A" shows "Maybe A" proof (cases xs) @@ -91,7 +91,7 @@ proof (cases xs) show "\<And>x. x: A \<Longrightarrow> some x: Maybe A" by intro qed -Definition tail: +Lemma (def) tail: assumes "A: U i" "xs: List A" shows "List A" proof (cases xs) @@ -128,7 +128,7 @@ Lemma tail_of_cons [comp]: subsection \<open>Append\<close> -Definition app: +Lemma (def) app: assumes "A: U i" "xs: List A" "ys: List A" shows "List A" apply (elim xs) @@ -143,7 +143,7 @@ translations "app" \<leftharpoondown> "CONST List.app A" subsection \<open>Map\<close> -Definition map: +Lemma (def) map: assumes "A: U i" "B: U i" "f: A \<rightarrow> B" "xs: List A" shows "List B" proof (elim xs) @@ -165,7 +165,7 @@ Lemma map_type [type]: subsection \<open>Reverse\<close> -Definition rev: +Lemma (def) rev: assumes "A: U i" "xs: List A" shows "List A" apply (elim xs) diff --git a/mltt/lib/Maybe.thy b/mltt/lib/Maybe.thy index 452acc2..257bc8f 100644 --- a/mltt/lib/Maybe.thy +++ b/mltt/lib/Maybe.thy @@ -17,7 +17,7 @@ lemma Maybe_some: "a: A \<Longrightarrow> some A a: Maybe A" unfolding Maybe_def none_def some_def by typechk+ -Definition MaybeInd: +Lemma (def) MaybeInd: assumes "A: U i" "\<And>m. m: Maybe A \<Longrightarrow> C m: U i" diff --git a/mltt/lib/Prelude.thy b/mltt/lib/Prelude.thy index 0393968..86165cd 100644 --- a/mltt/lib/Prelude.thy +++ b/mltt/lib/Prelude.thy @@ -100,7 +100,7 @@ Lemma unfolding Bool_def true_def false_def by typechk+ \<comment> \<open>Definitions like these should be handled by a future function package\<close> -Definition ifelse [rotated 1]: +Lemma (def) ifelse [rotated 1]: assumes *[unfolded Bool_def true_def false_def]: "\<And>x. x: Bool \<Longrightarrow> C x: U i" "x: Bool" |