Smaller formulae.

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index 20d069caa6be1a0038dbc4b21618fbc25fdc252f..81f0f07c7a20c2e306a74e68e9612d3b2bde8973 100644 (file)
--- a/helm/software/matita/nlibrary/sets/sets.ma
+++ b/helm/software/matita/nlibrary/sets/sets.ma
@@ -41,11 +41,11 @@ ndefinition powerset_setoid1: setoid → setoid1.
   [ napply (Ω \sup S)
   | napply mk_equivalence_relation1
      [ #A; #B; napply (∀x. iff (x ∈ A) (x ∈ B))
-     | nnormalize; #x; #x0; napply mk_iff; #H; nassumption
-     | nnormalize; #x; #y; #H; #A; napply mk_iff; #K
+     | nwhd; #x; #x0; napply mk_iff; #H; nassumption
+     | nwhd; #x; #y; #H; #A; napply mk_iff; #K
         [ napply (fi ?? (H ?)) | napply (if ?? (H ?)) ]
         nassumption
-     | nnormalize; #A; #B; #C; #H1; #H2; #H3; napply mk_iff; #H4
+     | nwhd; #A; #B; #C; #H1; #H2; #H3; napply mk_iff; #H4
         [ napply (if ?? (H2 ?)); napply (if ?? (H1 ?)); nassumption
         | napply (fi ?? (H1 ?)); napply (fi ?? (H2 ?)); nassumption]##]
 nqed.
@@ -69,8 +69,8 @@ interpretation "overlaps" 'overlaps U V = (overlaps ? U V).
 
 ndefinition intersects ≝ λA.λU,V:Ω \sup A. {x | x ∈ U ∧ x ∈ V }.
  #a; #a'; #H; napply mk_iff; *; #H1; #H2
-  [ napply (. ((H^-1‡#)‡(H^-1‡#))); nnormalize; napply conj; nassumption
-  | napply (. ((H‡#)‡(H‡#))); nnormalize; napply conj; nassumption]
+  [ napply (. ((H^-1‡#)‡(H^-1‡#))); nwhd; napply conj; nassumption
+  | napply (. ((H‡#)‡(H‡#))); nwhd; napply conj; nassumption]
 nqed.
   
 (*interpretation "intersects" 'intersects U V = (intersects ? U V).*)