Hmmm: I don't see much gain here.

diff --git a/helm/software/matita/nlibrary/algebra/magmas.ma b/helm/software/matita/nlibrary/algebra/magmas.ma
index 103d1755748e334d717e31c41a016b9fae644b07..24203f2098422059a1fc6ec95396267cb5b0b91b 100644 (file)
--- a/helm/software/matita/nlibrary/algebra/magmas.ma
+++ b/helm/software/matita/nlibrary/algebra/magmas.ma
@@ -20,19 +20,24 @@ nrecord magma_type : Type[1] ≝
  }.
 
 nrecord magma (A: magma_type) : Type[1] ≝
- { mcarr:> Ω \sup A;
+ { mcarr:> qpowerclass A;
    op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
  }.
-(* le coercion non vanno; sospetto setoid1_of_setoid *)
+
+ncoercion mcarr' : ∀A. ∀M: magma A. carr1 (qpowerclass_setoid (mtcarr A))
+ ≝ λA.λM: magma A.mcarr ? M
+ on _M: magma ? to carr1 (qpowerclass_setoid (mtcarr ?)).
+
 nrecord magma_morphism_type (A,B: magma_type) : Type[0] ≝
  { mmcarr:> unary_morphism A B;
-   mmprop: ∀x,y:carr A. mmcarr (op ? x y) = op … (mmcarr x) (mmcarr y)
+   mmprop: ∀x,y:A. mmcarr (op ? x y) = op … (mmcarr x) (mmcarr y)
  }.
-(* le coercion non vanno *)
+
 nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type[0] ≝
  { mmmcarr:> magma_morphism_type A B;
-   mmclosed: ∀x:carr A. x ∈ mcarr ? Ma → mmmcarr x ∈ mcarr ? Mb
+   mmclosed: ∀x:A. x ∈ mcarr ? Ma → mmmcarr x ∈ mcarr ? Mb
  }.
+
 (*
 ndefinition mm_image:
  ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism … Ma Mb → magma B.
@@ -68,7 +73,7 @@ nqed.
 ndefinition m_intersect: ∀A. magma A → magma A → magma A.
  #A; #M1; #M2;
  napply (mk_magma …)
-  [ napply (intersects_ok ? M1 M2)
+  [ napply (intersect_ok ? M1 M2)
   | #x; #y; nwhd in ⊢ (% → % → %); *; #Hx1; #Hx2; *; #Hy1; #Hy2;
     napply conj; napply op_closed; nassumption ]
 nqed.
\ No newline at end of file