From de1ac2d7795925edb488e4fac30d5e80537bfe33 Mon Sep 17 00:00:00 2001
From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Tue, 4 Aug 2009 19:47:46 +0000
Subject: [PATCH] Hmmm, quite broken now.

---
 .../matita/nlibrary/algebra/magmas.ma         | 33 +++++++++++--------
 1 file changed, 20 insertions(+), 13 deletions(-)

diff --git a/helm/software/matita/nlibrary/algebra/magmas.ma b/helm/software/matita/nlibrary/algebra/magmas.ma
index a879679a9..f3d3fe352 100644
--- a/helm/software/matita/nlibrary/algebra/magmas.ma
+++ b/helm/software/matita/nlibrary/algebra/magmas.ma
@@ -15,27 +15,33 @@
 include "sets/sets.ma".
 
 nrecord magma_type : Type[1] ≝
- { mcarr:> setoid;
-   op: mcarr → mcarr → mcarr
+ { mtcarr:> setoid;
+   op: binary_morphism mtcarr mtcarr mtcarr
  }.
 
 nrecord magma (A: magma_type) : Type[1] ≝
  { mcarr:> powerset_setoid1 A;
    op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
  }.
-
-nrecord magma_morphism_type (A,B: magma_type) : Type ≝
- { mmcarr:1> A → B;
-   mmprop: ∀x,y. mmcarr (op … x y) = op … (mmcarr x) (mmcarr y)
+(* le coercion non vanno; sospetto setoid1_of_setoid *)
+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)
  }.
-
-nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type ≝
+(* 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. x ∈ Ma → mmmcarr x ∈ Mb
+   mmclosed: ∀x:carr A. x ∈ mcarr ? Ma → mmmcarr x ∈ mcarr ? Mb
  }.
- 
-ndefinition image: ∀A,B. (A → B) → Ω \sup A → Ω \sup B ≝
- λA,B,f,Sa. {y | ∃x. x ∈ Sa ∧ f x = y}.
+(*
+(* 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.
@@ -76,4 +82,5 @@ ndefinition m_intersect: ∀A. magma A → magma A → magma A.
   [ napply (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
-- 
2.39.2