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[helm.git] / helm / software / matita / nlibrary / sets / sets.ma

diff --git a/helm/software/matita/nlibrary/sets/sets.ma b/helm/software/matita/nlibrary/sets/sets.ma
index 20d069caa6be1a0038dbc4b21618fbc25fdc252f..20065cec4156afcc5f9b974968dd99f1a3bb17ae 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).*)
@@ -82,4 +82,18 @@ interpretation "union" 'union U V = (union ? U V).
 
 ndefinition singleton ≝ λA:setoid.λa:A.{b | a=b}.
 
-interpretation "singleton" 'singl a = (singleton ? a).*)
\ No newline at end of file
+interpretation "singleton" 'singl a = (singleton ? a).*)
+
+(*
+(* qui non funziona una cippa *)
+ndefinition image: ∀A,B. (carr A → carr B) → Ω \sup A → Ω \sup B ≝
+ λA,B:setoid.λf:carr A → carr B.λSa:Ω \sup A.
+  {y | ∃x. x ∈ Sa ∧ eq_rel (carr B) (eq B) ? ?(*(f x) y*)}.
+  ##[##2: napply (f x); ##|##3: napply y]
+ #a; #a'; #H; nwhd; nnormalize; (* per togliere setoid1_of_setoid *) napply (mk_iff ????);
+ *; #x; #Hx; napply (ex_intro … x)
+  [ napply (. (#‡(#‡#))); 
+
+ndefinition counter_image: ∀A,B. (A → B) → Ω \sup B → Ω \sup A ≝
+ λA,B,f,Sb. {x | ∃y. y ∈ Sb ∧ f x = y}.
+*)