update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / pnat_plus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/pnat_plus.ma b/matita/matita/contribs/lambdadelta/ground/arith/pnat_plus.ma
index eead7943bb2a50d4859b90c3cb6ff2aad0719f63..8fd6b5c47034a1cf6783ab55845b669dce8e9513 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/arith/pnat_plus.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/pnat_plus.ma
@@ -14,16 +14,16 @@
 
 include "ground/arith/pnat_iter.ma".
 
-(* POSITIVE INTEGERS ********************************************************)
+(* ADDITION FOR POSITIVE INTEGERS *******************************************)
 
 definition pplus: pnat → pnat → pnat ≝
            λp,q. psucc^q p.
 
 interpretation
-  "plus (positive integers"
+  "plus (positive integers)"
   'plus p q = (pplus p q).
 
-(* Basic rewrites ***********************************************************)
+(* Basic constructions ******************************************************)
 
 lemma pplus_one_dx (p): ↑p = p + 𝟏.
 // qed.
@@ -31,7 +31,7 @@ lemma pplus_one_dx (p): ↑p = p + 𝟏.
 lemma pplus_succ_dx (p) (q): ↑(p+q) = p + ↑q.
 // qed.
 
-(* Semigroup properties *****************************************************)
+(* Advanced constructions (semigroup properties) ****************************)
 
 lemma pplus_succ_sn (p) (q): ↑(p+q) = ↑p + q.
 #p #q @(piter_appl … psucc)
@@ -43,7 +43,7 @@ qed.
 
 lemma pplus_comm: commutative … pplus.
 #p elim p -p //
-qed.
+qed-. (* * gets in the way with auto *)
 
 lemma pplus_assoc: associative … pplus.
 #p #q #r elim r -r //