X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Flib%2Farithmetics%2Fnat.ma;h=6fa6d57a8e78b130ae818438e644254019bee790;hb=21de0d35017656c5a55528390b54b0b2ae395b44;hp=6b3a1a19bf7b730af3e90aacec9d36b48a3d0289;hpb=cacbe3c6493ddce76c4c13379ade271d8dd172e8;p=helm.git diff --git a/matitaB/matita/lib/arithmetics/nat.ma b/matitaB/matita/lib/arithmetics/nat.ma index 6b3a1a19b..6fa6d57a8 100644 --- a/matitaB/matita/lib/arithmetics/nat.ma +++ b/matitaB/matita/lib/arithmetics/nat.ma @@ -22,7 +22,7 @@ alias num (instance 0) = "natural number". definition pred ≝ λn. match n with [ O ⇒ O | S p ⇒ p]. -theorem pred_Sn : ∀n. n = pred (S n). +theorem pred_Sn : ∀n.n = pred (S n). // qed. theorem injective_S : injective nat nat S. @@ -76,7 +76,7 @@ theorem plus_Sn_m: ∀n,m:nat. S (n + m) = S n + m. // qed. *) -theorem plus_n_O: ∀n:nat. n = n+O. +theorem plus_n_O: ∀n:nat. n = n+0. #n (elim n) normalize // qed. theorem plus_n_Sm : ∀n,m:nat. S (n+m) = n + S m.