update in groud_2 and models

[helm.git] / helm / software / matita / nlibrary / nat / plus.ma

diff --git a/helm/software/matita/nlibrary/nat/plus.ma b/helm/software/matita/nlibrary/nat/plus.ma
index 809288f2a7bb7d6be2f39ab211811db124164a0b..8bbc71b9cbbbc3b5d50ece774467c69ebf890048 100644 (file)
--- a/helm/software/matita/nlibrary/nat/plus.ma
+++ b/helm/software/matita/nlibrary/nat/plus.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "nat/nat.ma".
+include "nat/big_ops.ma".
 include "algebra/unital_magmas.ma".
 include "algebra/abelian_magmas.ma".
 
@@ -21,6 +21,8 @@ nlet rec plus (n:nat) (m:nat) on n : nat ≝
   [ O ⇒ m
   | S n' ⇒ S (plus n' m) ].
 
+interpretation "natural plus" 'plus x y = (plus x y).
+
 ndefinition plus_magma_type: magma_type.
  napply mk_magma_type
   [ napply NAT
@@ -50,4 +52,6 @@ ndefinition plus_unital_magma_type: unital_magma_type.
   | napply O
   | #x; napply refl
   | #x; (* qua manca ancora l'hint *) napply (symm plus_abelian_magma_type) ]
-nqed.
\ No newline at end of file
+nqed.
+
+ndefinition big_plus ≝ λn.λf.big_op plus_magma_type n f O.