diff options
| author | coq | 2001-04-23 15:07:44 +0000 |
|---|---|---|
| committer | coq | 2001-04-23 15:07:44 +0000 |
| commit | a3837fa9dd60b7b8528e2e31c98682528c694dcd (patch) | |
| tree | 9b51b3054b6844a2f346d23a199828ba49ea8097 /theories/IntMap/Map.v | |
| parent | 5993237b592c726d6777608623a7cc063b1dabb9 (diff) | |
Minor layout adjustments for Library doc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1672 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/IntMap/Map.v')
| -rw-r--r-- | theories/IntMap/Map.v | 25 |
1 files changed, 15 insertions, 10 deletions
diff --git a/theories/IntMap/Map.v b/theories/IntMap/Map.v index 05f5612ab4..245ceb558e 100644 --- a/theories/IntMap/Map.v +++ b/theories/IntMap/Map.v @@ -58,6 +58,7 @@ Section MapDefs. end. Definition newMap := M0. + Definition MapSingleton := M1. Definition eqm := [g,g':ad->option] (a:ad) (g a)=(g' a). @@ -78,14 +79,14 @@ Section MapDefs. Unfold MapGet. Intros. Rewrite (ad_eq_correct a). Reflexivity. Qed. - Lemma M1_semantics_2 - : (a,a':ad) (y:A) (ad_eq a a')=false -> (MapGet (M1 a y) a')=NONE. + Lemma M1_semantics_2 : + (a,a':ad) (y:A) (ad_eq a a')=false -> (MapGet (M1 a y) a')=NONE. Proof. Intros. Simpl. Rewrite H. Reflexivity. Qed. - Lemma Map2_semantics_1 - : (m,m':Map) (eqm (MapGet m) [a:ad] (MapGet (M2 m m') (ad_double a))). + Lemma Map2_semantics_1 : + (m,m':Map) (eqm (MapGet m) [a:ad] (MapGet (M2 m m') (ad_double a))). Proof. Unfold eqm. Induction a; Trivial. Qed. @@ -99,8 +100,8 @@ Section MapDefs. Exact (Map2_semantics_1 m m' a). Qed. - Lemma Map2_semantics_2 - : (m,m':Map) (eqm (MapGet m') [a:ad] (MapGet (M2 m m') (ad_double_plus_un a))). + Lemma Map2_semantics_2 : + (m,m':Map) (eqm (MapGet m') [a:ad] (MapGet (M2 m m') (ad_double_plus_un a))). Proof. Unfold eqm. Induction a; Trivial. Qed. @@ -205,7 +206,8 @@ Section MapDefs. Qed. i*) - Lemma MapGet_if_same : (m:Map) (b:bool) (a:ad) (MapGet (if b then m else m) a)=(MapGet m a). + Lemma MapGet_if_same : (m:Map) (b:bool) (a:ad) + (MapGet (if b then m else m) a)=(MapGet m a). Proof. Induction b;Trivial. Qed. @@ -240,7 +242,8 @@ Section MapDefs. Qed. Lemma MapGet_M2_both_NONE : (m,m':Map) (a:ad) - (MapGet m (ad_div_2 a))=NONE -> (MapGet m' (ad_div_2 a))=NONE -> (MapGet (M2 m m') a)=NONE. + (MapGet m (ad_div_2 a))=NONE -> (MapGet m' (ad_div_2 a))=NONE -> + (MapGet (M2 m m') a)=NONE. Proof. Intros. Rewrite (Map2_semantics_3 m m' a). Case (ad_bit_0 a); Assumption. @@ -575,7 +578,8 @@ Section MapDefs. | (M2 m1 m2) => [m':Map] Cases m' of M0 => m | (M1 a' y') => (MapPut m a' y') - | (M2 m'1 m'2) => (M2 (MapMerge m1 m'1) (MapMerge m2 m'2)) + | (M2 m'1 m'2) => (M2 (MapMerge m1 m'1) + (MapMerge m2 m'2)) end end. @@ -659,7 +663,8 @@ Section MapDefs. Qed. Lemma MapDelta_semantics_1 : (m,m':Map) (a:ad) - (MapGet m a)=NONE -> (MapGet m' a)=NONE -> (MapGet (MapDelta m m') a)=NONE. + (MapGet m a)=NONE -> (MapGet m' a)=NONE -> + (MapGet (MapDelta m m') a)=NONE. Proof. Induction m. Trivial. Exact MapDelta_semantics_1_1. |
