X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Fsets%2Fpartitions.ma;h=61173c78e34215c0081b4d0a3a29f49bbd0db564;hb=6fe06927f3293bfce4a01a587abd9913e711da88;hp=e33ddfa1d00af461221edc4c86c4d8d4a6831de0;hpb=b91d9e60b0a5f450d2725d4b9bb3ed7f81ef6d3a;p=helm.git

diff --git a/helm/software/matita/nlibrary/sets/partitions.ma b/helm/software/matita/nlibrary/sets/partitions.ma
index e33ddfa1d..61173c78e 100644
--- a/helm/software/matita/nlibrary/sets/partitions.ma
+++ b/helm/software/matita/nlibrary/sets/partitions.ma
@@ -13,24 +13,26 @@
 (**************************************************************************)
 
 include "sets/sets.ma".
-include "nat/plus.ma". (* tempi biblici neggli include che fa plus.ma *)
+include "nat/plus.ma". 
 include "nat/compare.ma".
 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".
 nrecord partition (A: setoid) : Type[1] ≝ 
  { support: setoid;
    indexes: qpowerclass support;
    class: unary_morphism1 (setoid1_of_setoid support) (qpowerclass_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 ? ? (λx.class x) = full_set A
- }. napply indexes; nqed.
-
+   disjoint: ∀i,j. i ∈ indexes → j ∈ indexes → class i ≬ class j → i = j;
+   covers: big_union support ? indexes (λx.class x) = full_set A
+ }.
+ 
 naxiom daemon: False.
 
 nlet rec iso_nat_nat_union (s: nat → nat) m index on index : pair nat nat ≝
@@ -129,9 +131,10 @@ nlemma partition_splits_card:
  ∀A. ∀P:partition A. ∀n,s.
   ∀f:isomorphism ?? (Nat_ n) (indexes ? P).
    (∀i. isomorphism ?? (Nat_ (s i)) (class ? P (iso_f ???? f i))) →
-    (isomorphism ?? (Nat_ (big_plus n (λi.λ_.s i))) A).
- #A; #P; #Sn; ncases Sn
-  [ #s; #f; #fi; nlapply (covers ? P); *; #_; #H;
+    (isomorphism ?? (Nat_ (big_plus n (λi.λ_.s i))) (Full_set A)).
+#A; #P; #Sn; ncases Sn
+  [ #s; #f; #fi;
+    nlapply (covers ? P); *; #_; #H;
     (*
     nlapply
      (big_union_preserves_iso ??? (indexes A P) (Nat_ O) (λx.class ? P x) f);
@@ -139,7 +142,7 @@ nlemma partition_splits_card:
     nelim daemon (* impossibile *)
   | #n; #s; #f; #fi; @
   [ @
-     [ napply (λm.let p ≝ iso_nat_nat_union s m n in iso_f ???? (fi (fst … p)) (snd … p))
+     [ napply (λm.let p ≝ (iso_nat_nat_union s m n) in iso_f ???? (fi (fst … p)) (snd … p))
      | #a; #a'; #H; nrewrite < H; napply refl ]
 ##| #x; #Hx; nwhd; napply I
 ##| #y; #_;
@@ -147,12 +150,14 @@ nlemma partition_splits_card:
     ngeneralize in match (Hc y I) in ⊢ ?; *; #index; *; #Hi1; #Hi2;
     ngeneralize in match (f_sur ???? f ? Hi1) in ⊢ ?; *; #nindex; *; #Hni1; #Hni2;
     ngeneralize in match (f_sur ???? (fi nindex) y ?) in ⊢ ?
-     [##2: napply (. #‡(†?));##[##3: napply Hni2 |##2: ##skip | nassumption]##]
+     [##2: alias symbol "refl" = "refl".
+alias symbol "prop1" = "prop11".
+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);
     napply (ex_intro … xxx); napply conj
      [ napply iso_nat_nat_union_pre [ napply le_S_S_to_le; nassumption | nassumption ]
-   ##| nwhd in ⊢ (???%%); napply (.= ?) [ nassumption|##skip]
+   ##| nwhd in ⊢ (???%%); napply (.= ?) [##3: nassumption|##skip]
        ngeneralize in match (iso_nat_nat_union_char n s xxx ?) in ⊢ ?
         [##2: napply iso_nat_nat_union_pre [ napply le_S_S_to_le; nassumption | nassumption]##]
        *; *; #K1; #K2; #K3;
@@ -168,7 +173,7 @@ nlemma partition_splits_card:
       ngeneralize in match (disjoint ? P (iso_f ???? f i1) (iso_f ???? f i1') ???) in ⊢ ?
        [##2,3: napply f_closed; nassumption
        |##4: napply ex_intro [ napply (iso_f ???? (fi i1) i2) ] napply conj
-         [ napply f_closed; nassumption ##| napply (. ?‡#) [##2: nassumption | ##3: ##skip]
+         [ napply f_closed; nassumption ##| napply (. ?‡#) [ nassumption | ##2: ##skip]
          nwhd; napply f_closed; nassumption]##]
       #E'; ngeneralize in match (? : i1=i1') in ⊢ ?
        [##2: napply (f_inj … E'); nassumption
@@ -204,4 +209,4 @@ ndefinition partition_of_compatible_equivalence_relation:
     napply sym; nassumption
   | nnormalize; napply conj
      [ #a; #_; napply I | #a; #_; napply (ex_intro … a); napply conj [ napply I | napply refl]##]
-nqed.
\ No newline at end of file
+nqed.