New tactics ncut and nlapply.

[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 e83175f18921ac5675134fda93b77ce979ed9d69..e33ddfa1d00af461221edc4c86c4d8d4a6831de0 100644 (file)
--- a/helm/software/matita/nlibrary/sets/partitions.ma
+++ b/helm/software/matita/nlibrary/sets/partitions.ma
@@ -22,11 +22,6 @@ include "datatypes/pairs.ma".
 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".
-alias symbol "eq" = "setoid eq".
-alias symbol "eq" = "setoid1 eq".
 nrecord partition (A: setoid) : Type[1] ≝ 
  { support: setoid;
    indexes: qpowerclass support;
@@ -63,7 +58,6 @@ naxiom ad_hoc15: ∀a,a',b,c. a=a' → b < c → a + b < c + a'.
 naxiom ad_hoc16: ∀a,b,c. a < c → a < b + c.
 naxiom not_lt_to_le: ∀a,b. ¬ (a < b) → b ≤ a.
 naxiom le_to_le_S_S: ∀a,b. a ≤ b → S a ≤ S b.
-naxiom minus_S_S: ∀a,b. S a - S b = a - b.
 naxiom minus_S: ∀n. S n - n = S O.
 naxiom ad_hoc17: ∀a,b,c,d,d'. a+c+d=b+c+d' → a+d=b+d'.
 naxiom split_big_plus:
@@ -81,8 +75,8 @@ ntheorem iso_nat_nat_union_char:
     fst … p ≤ n ∧ snd … p < s (fst … p).
  #n; #s; nelim n
   [ #m; nwhd in ⊢ (??% → let p ≝ % in ?); nwhd in ⊢ (??(??%) → ?);
-    nrewrite > (plus_n_O (s O)); #H; nrewrite > (ltb_t … H); nnormalize;
-    napply conj [ napply conj [ napply refl | napply le_n ] ##| nassumption ]
+    nrewrite > (plus_n_O (s O)); #H; nrewrite > (ltb_t … H); nnormalize; @
+    [ @ [ napply refl | napply le_n ] ##| nassumption ]
 ##| #n'; #Hrec; #m; nwhd in ⊢ (??% → let p ≝ % in ?); #H;
     ncases (ltb_cases m (s (S n'))); *; #H1; #H2; nrewrite > H2;
     nwhd in ⊢ (let p ≝ % in ?); nwhd
@@ -91,10 +85,10 @@ ntheorem iso_nat_nat_union_char:
         | nnormalize; napply le_n]
       ##| nnormalize; nassumption ]
    ##| nchange in H with (m < s (S n') + big_plus (S n') (λi.λ_.s i));
-       ngeneralize in match (Hrec (m - s (S n')) ?) in ⊢ ?
-        [##2: napply ad_hoc9; nassumption] *; *; #Hrec1; #Hrec2; #Hrec3; napply conj
+       nlapply (Hrec (m - s (S n')) ?)
+        [ napply ad_hoc9; nassumption] *; *; #Hrec1; #Hrec2; #Hrec3; @
         [##2: nassumption
-        |napply conj
+        |@
          [nrewrite > (split_big_plus …); ##[##2:napply ad_hoc11;##|##3:##skip]
           nrewrite > (ad_hoc12 …); ##[##2: nassumption]
           nwhd in ⊢ (????(?(??%)?));
@@ -135,17 +129,16 @@ 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))) (Full_set A)).
- STOP #A; #P; #Sn; ncases Sn
-  [ #s; #f; #fi;
-    ngeneralize in match (covers ? P) in ⊢ ?; *; #_; #H;
+    (isomorphism ?? (Nat_ (big_plus n (λi.λ_.s i))) A).
+ #A; #P; #Sn; ncases Sn
+  [ #s; #f; #fi; nlapply (covers ? P); *; #_; #H;
     (*
-    ngeneralize in match
-     (big_union_preserves_iso ??? (indexes A P) (Nat_ O) (λx.class ? P x) f) in ⊢ ?;
+    nlapply
+     (big_union_preserves_iso ??? (indexes A P) (Nat_ O) (λx.class ? P x) f);
      *; #K; #_; nwhd in K: (? → ? → %);*)
     nelim daemon (* impossibile *)
-  | #n; #s; #f; #fi; napply mk_isomorphism
-  [ napply mk_unary_morphism
+  | #n; #s; #f; #fi; @
+  [ @
      [ 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