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=28b3795c88098743ba2648392ff77ef04c1244b1;hpb=28da21926eb9cab187ba8a64999c760083f60369;p=helm.git

diff --git a/helm/software/matita/nlibrary/algebra/magmas.ma b/helm/software/matita/nlibrary/algebra/magmas.ma
index 28b3795c8..685d62480 100644
--- a/helm/software/matita/nlibrary/algebra/magmas.ma
+++ b/helm/software/matita/nlibrary/algebra/magmas.ma
@@ -14,63 +14,72 @@
 
 include "sets/sets.ma".
 
-nrecord pre_magma : Type[1] ≝
- { carr: Type;
-   op: carr → carr → carr
+nrecord magma_type : Type[1] ≝
+ { mtcarr:> setoid;
+   op: unary_morphism mtcarr (unary_morph_setoid mtcarr mtcarr)
  }.
-(* this is a projection *)
-ndefinition carr ≝ λM: pre_magma. match M with [ mk_pre_magma carr _ ⇒ carr ].
-ndefinition op ≝
- λM: pre_magma. match M return λM. carr M → carr M → carr M with [ mk_pre_magma _ op ⇒ op ].
-(* ncoercion carr. *)
 
-nrecord magma (A: pre_magma) : Type[1] ≝
- { mcarr: Ω \sup (carr A);
+nrecord magma (A: magma_type) : Type[1] ≝
+ { mcarr:> ext_powerclass A;
    op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
  }.
-(* this is a projection *)
-ndefinition mcarr ≝ λA.λM: magma A. match M with [ mk_magma mcarr _ ⇒ mcarr ].
-ndefinition op_closed ≝
- λA.λM: magma A.
-  match M return λM.∀x,y. x ∈ mcarr ? M → y ∈ mcarr ? M → op A x y ∈ mcarr ? M with
-   [ mk_magma _ opc ⇒ opc ].
 
-nrecord pre_magma_morphism (A,B: pre_magma) : Type ≝
- { mmcarr: carr A → carr B;
-   mmprop: ∀x,y. mmcarr (op ? x y) = op ? (mmcarr x) (mmcarr y)
- }.
-(* this is a projection *)
-ndefinition mmcarr ≝
- λA,B.λf: pre_magma_morphism A B. match f with [ mk_pre_magma_morphism f _ ⇒ f ].
+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 (A) (B) (Ma: magma A) (Mb: magma B) : Type ≝
- { mmmcarr: pre_magma_morphism A B;
-   mmclosed: ∀x. x ∈ mcarr ? Ma → mmcarr ?? mmmcarr x ∈ mcarr ? Mb
+nrecord magma_morphism_type (A,B: magma_type) : Type[0] ≝
+ { mmcarr:> unary_morphism A B;
+   mmprop: ∀x,y:A. mmcarr (op ? x y) = op … (mmcarr x) (mmcarr y)
  }.
-(* this is a projection *)
-ndefinition mmmcarr ≝
- λA,B,Ma,Mb.λf: magma_morphism A B Ma Mb. match f with [ mk_magma_morphism f _ ⇒ f ].
-ndefinition mmclosed ≝
- λA,B,Ma,Mb.λf: magma_morphism A B Ma Mb.
-  match f return λf.∀x. x ∈ mcarr ? Ma → mmcarr ?? (mmmcarr ???? f) x ∈ mcarr ? Mb with
-   [ mk_magma_morphism _ p ⇒ p ].
- 
-ndefinition sub_magma ≝
- λA.λM1,M2: magma A. ∀x. x ∈ mcarr ? M1 → x ∈ mcarr ? M2.
- 
-ndefinition image: ∀A,B. (A → B) → Ω \sup A → Ω \sup B ≝
- λA,B,f,Sa. {y | ∃x. x ∈ Sa ∧ f x = y}.
 
-naxiom daemon: False.
+nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type[0] ≝
+ { mmmcarr:> magma_morphism_type A B;
+   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.
+ ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism … Ma Mb → magma B.
  #A; #B; #Ma; #Mb; #f;
- napply (mk_magma ???)
-  [ napply (image ?? (mmcarr ?? (mmmcarr ???? f)) (mcarr ? Ma)) 
-  | #x; #y; *; #x0; #Hx0; *; #y0; #Hy0; nwhd;
-    napply (ex_intro ????)
-     [ napply (op ? x0 y0) 
-     | napply (conj ????);
-       nelim daemon ]##]
+ napply mk_magma
+  [ napply (image … f Ma)
+  | #x; #y; nwhd in ⊢ (% → % → ?); *; #x0; *; #Hx0; #Hx1; *; #y0; *; #Hy0; #Hy1; nwhd;
+    napply ex_intro
+     [ napply (op … x0 y0) 
+     | napply conj
+        [ napply op_closed; nassumption
+        | nrewrite < Hx1;
+          nrewrite < Hy1;
+          napply (mmprop … f)]##]
+nqed.
+
+ndefinition mm_counter_image:
+ ∀A,B. ∀Ma: magma A. ∀Mb: magma B. magma_morphism … Ma Mb → magma A.
+  #A; #B; #Ma; #Mb; #f;
+  napply mk_magma
+   [ napply (counter_image … f Mb)
+   | #x; #y; nwhd in ⊢ (% → % → ?); *; #x0; *; #Hx0; #Hx1; *; #y0; *; #Hy0; #Hy1; nwhd;
+     napply ex_intro
+      [ napply (op … x0 y0)
+      | napply conj
+         [ napply op_closed; nassumption
+         | nrewrite < Hx1;
+           nrewrite < Hy1;
+           napply (mmprop … f)]##]
+nqed.
+*)
+
+ndefinition m_intersect: ∀A. magma A → magma A → magma A.
+ #A; #M1; #M2;
+ napply (mk_magma …)
+  [ 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