X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Fsets%2Fpartitions.ma;h=95145b11b4e150ca6d1b86d9069fa2cc274f9c22;hb=bac3136bf99a18374b91e1ec900e455567e8f741;hp=c1092c497cb355e766a188c8f3c59b1862f8c961;hpb=32af98424d4320a4a38fff23ac0398e026fe0ffc;p=helm.git

diff --git a/helm/software/matita/nlibrary/sets/partitions.ma b/helm/software/matita/nlibrary/sets/partitions.ma
index c1092c497..95145b11b 100644
--- a/helm/software/matita/nlibrary/sets/partitions.ma
+++ b/helm/software/matita/nlibrary/sets/partitions.ma
@@ -19,17 +19,12 @@ include "nat/minus.ma".
 include "datatypes/pairs.ma".
 
 alias symbol "eq" = "setoid eq".
-
 alias symbol "eq" = "setoid1 eq".
 alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
 nrecord partition (A: setoid) : Type[1] ≝ 
  { support: setoid;
-   indexes: qpowerclass support;
-   class: unary_morphism1 (setoid1_of_setoid support) (qpowerclass_setoid A);
+   indexes: ext_powerclass support;
+   class: unary_morphism1 (setoid1_of_setoid support) (ext_powerclass_setoid A);
    inhabited: ∀i. i ∈ indexes → class i ≬ class i;
    disjoint: ∀i,j. i ∈ indexes → j ∈ indexes → class i ≬ class j → i = j;
    covers: big_union support ? indexes (λx.class x) = full_set A
@@ -154,6 +149,7 @@ nlemma partition_splits_card:
     nlapply (f_sur ???? (fi nindex) y ?)
      [ alias symbol "refl" = "refl".
 alias symbol "prop1" = "prop11".
+alias symbol "prop2" = "prop21 mem".
 napply (. #‡(†?));##[##2: napply Hni2 |##1: ##skip | nassumption]##]
     *; #nindex2; *; #Hni21; #Hni22;
     nletin xxx ≝ (plus (big_plus (minus n nindex) (λi.λ_.s (S (plus i nindex)))) nindex2);
@@ -170,12 +166,13 @@ napply (. #‡(†?));##[##2: napply Hni2 |##1: ##skip | nassumption]##]
         |##5: napply le_S_S_to_le; nassumption
         |##*: nassumption]##]
 ##| #x; #x'; nnormalize in ⊢ (? → ? → %); #Hx; #Hx'; #E;
-    ncut(∀i1,i2,i1',i2'. i1 ∈ Nat_ (S n) → i1' ∈ Nat_ (S n) → i2 ∈ pc ? (Nat_ (s i1)) → i2' ∈ pc ? (Nat_ (s i1')) → eq_rel (carr A) (eq A) (iso_f ???? (fi i1) i2) (iso_f ???? (fi i1') i2') → i1=i1' ∧ i2=i2');
+    ncut(∀i1,i2,i1',i2'. i1 ∈ Nat_ (S n) → i1' ∈ Nat_ (S n) → i2 ∈ Nat_ (s i1) → i2' ∈ Nat_ (s i1') → eq_rel (carr A) (eq A) (fi i1 i2) (fi i1' i2') → i1=i1' ∧ i2=i2');
     ##[ #i1; #i2; #i1'; #i2'; #Hi1; #Hi1'; #Hi2; #Hi2'; #E;
        nlapply(disjoint … P (f i1) (f i1') ???)
        [##2,3: napply f_closed; nassumption
        |##1: @ (fi i1 i2); @;
-         ##[ napply f_closed; nassumption ##| napply (. E‡#);
+         ##[ napply f_closed; nassumption ##| alias symbol "refl" = "refl1".
+napply (. E‡#);
              nwhd; napply f_closed; nassumption]##]
       #E'; ncut(i1 = i1'); ##[ napply (f_inj … E'); nassumption; ##]
       #E''; nrewrite < E''; @; 
@@ -202,7 +199,7 @@ ndefinition partition_of_compatible_equivalence_relation:
   [ napply (quotient ? R)
   | napply Full_set
   | napply mk_unary_morphism1
-     [ #a; napply mk_qpowerclass
+     [ #a; napply mk_ext_powerclass
         [ napply {x | R x a}
         | #x; #x'; #H; nnormalize; napply mk_iff; #K; nelim daemon]
    ##| #a; #a'; #H; napply conj; #x; nnormalize; #K [ nelim daemon | nelim daemon]##]