X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Fsets%2Fpartitions.ma;h=61173c78e34215c0081b4d0a3a29f49bbd0db564;hb=6fe06927f3293bfce4a01a587abd9913e711da88;hp=40ecd43b43ec88377f22796f37a77555cfb54c53;hpb=8049c166a37789d7a1b1ca1c3a1174712bbf87ba;p=helm.git

diff --git a/helm/software/matita/nlibrary/sets/partitions.ma b/helm/software/matita/nlibrary/sets/partitions.ma
index 40ecd43b4..61173c78e 100644
--- a/helm/software/matita/nlibrary/sets/partitions.ma
+++ b/helm/software/matita/nlibrary/sets/partitions.ma
@@ -18,12 +18,10 @@ include "nat/compare.ma".
 include "nat/minus.ma".
 include "datatypes/pairs.ma".
 
-alias symbol "eq" (instance 2) = "leibnitz's equality".
-alias symbol "eq" (instance 1) = "setoid eq".
 alias symbol "eq" = "setoid eq".
+
 alias symbol "eq" = "setoid1 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] ≝ 
@@ -31,10 +29,10 @@ nrecord partition (A: setoid) : Type[1] ≝
    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 ≝
@@ -136,7 +134,7 @@ nlemma partition_splits_card:
     (isomorphism ?? (Nat_ (big_plus n (λi.λ_.s i))) (Full_set A)).
 #A; #P; #Sn; ncases Sn
   [ #s; #f; #fi;
-    ngeneralize in match (covers ? P) in ⊢ ?; *; #_; #H;
+    nlapply (covers ? P); *; #_; #H;
     (*
     nlapply
      (big_union_preserves_iso ??? (indexes A P) (Nat_ O) (λx.class ? P x) f);
@@ -152,7 +150,9 @@ 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 (. #‡(†?));##[##2: napply Hni2 |##1: ##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