- fixed bug in coercion application, input/output swapped in unification

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

diff --git a/helm/software/matita/nlibrary/sets/partitions.ma b/helm/software/matita/nlibrary/sets/partitions.ma
index 61173c78e34215c0081b4d0a3a29f49bbd0db564..93f9cd6b5d3e014121adf9ff04042816848cb5a6 100644 (file)
--- a/helm/software/matita/nlibrary/sets/partitions.ma
+++ b/helm/software/matita/nlibrary/sets/partitions.ma
@@ -24,6 +24,7 @@ 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".
 nrecord partition (A: setoid) : Type[1] ≝ 
  { support: setoid;
    indexes: qpowerclass support;
@@ -146,25 +147,25 @@ nlemma partition_splits_card:
      | #a; #a'; #H; nrewrite < H; napply refl ]
 ##| #x; #Hx; nwhd; napply I
 ##| #y; #_;
-    ngeneralize in match (covers ? P) in ⊢ ?; *; #_; #Hc;
-    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: alias symbol "refl" = "refl".
+    nlapply (covers ? P); *; #_; #Hc;
+    nlapply (Hc y I); *; #index; *; #Hi1; #Hi2;
+    nlapply (f_sur ???? f ? Hi1); *; #nindex; *; #Hni1; #Hni2;
+    nlapply (f_sur ???? (fi nindex) y ?)
+     [ 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
+    @ xxx; @
      [ napply iso_nat_nat_union_pre [ napply le_S_S_to_le; nassumption | nassumption ]
    ##| 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]##]
+       nlapply (iso_nat_nat_union_char n s xxx ?)
+        [napply iso_nat_nat_union_pre [ napply le_S_S_to_le; nassumption | nassumption]##]
        *; *; #K1; #K2; #K3;
-       ngeneralize in match
+       nlapply
         (iso_nat_nat_union_uniq n s nindex (fst … (iso_nat_nat_union s xxx n))
-          nindex2 (snd … (iso_nat_nat_union s xxx n)) ?????) in ⊢ ?
-        [ *; #E1; #E2; nrewrite > E1; nrewrite > E2; napply refl
+          nindex2 (snd … (iso_nat_nat_union s xxx n)) ?????)
+        [##2: *; #E1; #E2; nrewrite > E1; nrewrite > E2; napply refl
         | napply le_S_S_to_le; nassumption
         |##*: nassumption]##]
 ##| #x; #x'; nnormalize in ⊢ (? → ? → %); #Hx; #Hx'; #E;