X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fnlibrary%2Falgebra%2Fmagmas.ma;h=685d6248059afb3e162ae4ec00ea1304f05318af;hb=14aa468ded0030440dbc9cc8fb5b936d927bb6fd;hp=f3d3fe3528a3c48bc1797b64913cc855f85a6456;hpb=de1ac2d7795925edb488e4fac30d5e80537bfe33;p=helm.git

diff --git a/helm/software/matita/nlibrary/algebra/magmas.ma b/helm/software/matita/nlibrary/algebra/magmas.ma
index f3d3fe352..685d62480 100644
--- a/helm/software/matita/nlibrary/algebra/magmas.ma
+++ b/helm/software/matita/nlibrary/algebra/magmas.ma
@@ -16,33 +16,35 @@ include "sets/sets.ma".
 
 nrecord magma_type : Type[1] ≝
  { mtcarr:> setoid;
-   op: binary_morphism mtcarr mtcarr mtcarr
+   op: unary_morphism mtcarr (unary_morph_setoid mtcarr mtcarr)
  }.
 
 nrecord magma (A: magma_type) : Type[1] ≝
- { mcarr:> powerset_setoid1 A;
+ { mcarr:> ext_powerclass A;
    op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
  }.
-(* le coercion non vanno; sospetto setoid1_of_setoid *)
+
+alias symbol "hint_decl" = "hint_decl_Type2".
+unification hint 0 ≔ 
+  A : ? ⊢ carr1 (ext_powerclass_setoid A) ≡ ext_powerclass A. 
+
+(*
+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
  }.
-(*
-(* qui non funziona una cippa *)
-ndefinition image: ∀A,B. (carr A → carr B) → Ω \sup A → Ω \sup B ≝
- λA,B:setoid.λf:carr A → carr B.λSa:Ω \sup A.
-  {y | ∃x. x ∈ Sa ∧ eq_rel (carr B) (eq B) ? ?(*(f x) y*)}.
-  ##[##2: napply (f x); ##|##3: napply y]
- #a; #a'; #H; nwhd; nnormalize; (* per togliere setoid1_of_setoid *) napply (mk_iff ????);
- *; #x; #Hx; napply (ex_intro … x)
-  [ napply (. (#‡(#‡#))); 
 
+(*
 ndefinition mm_image:
  ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism … Ma Mb → magma B.
  #A; #B; #Ma; #Mb; #f;
@@ -58,9 +60,6 @@ ndefinition mm_image:
           napply (mmprop … f)]##]
 nqed.
 
-ndefinition counter_image: ∀A,B. (A → B) → Ω \sup B → Ω \sup A ≝
- λA,B,f,Sb. {x | ∃y. y ∈ Sb ∧ f x = y}.
- 
 ndefinition mm_counter_image:
  ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism … Ma Mb → magma A.
   #A; #B; #Ma; #Mb; #f;
@@ -75,12 +74,12 @@ ndefinition mm_counter_image:
            nrewrite < Hy1;
            napply (mmprop … f)]##]
 nqed.
+*)
 
 ndefinition m_intersect: ∀A. magma A → magma A → magma A.
  #A; #M1; #M2;
  napply (mk_magma …)
-  [ napply (M1 ∩ M2)
+  [ napply (intersect_is_ext_morph ? M1 M2)
   | #x; #y; nwhd in ⊢ (% → % → %); *; #Hx1; #Hx2; *; #Hy1; #Hy2;
     napply conj; napply op_closed; nassumption ]
-nqed.
-*)
\ No newline at end of file
+nqed.
\ No newline at end of file