From aedc56735e526f858b6b5e6a7867674451cc0285 Mon Sep 17 00:00:00 2001
From: Claudio Sacerdoti Coen <claudio.sacerdoticoen@unibo.it>
Date: Fri, 24 Jul 2009 22:19:37 +0000
Subject: [PATCH] It works better now.

---
 .../matita/nlibrary/algebra/magmas.ma         | 19 ++++++++++++-------
 1 file changed, 12 insertions(+), 7 deletions(-)

diff --git a/helm/software/matita/nlibrary/algebra/magmas.ma b/helm/software/matita/nlibrary/algebra/magmas.ma
index 1c829997a..842cfceb9 100644
--- a/helm/software/matita/nlibrary/algebra/magmas.ma
+++ b/helm/software/matita/nlibrary/algebra/magmas.ma
@@ -14,29 +14,26 @@
 
 include "sets/sets.ma".
 
-nrecord pre_magma : Type[1] ≝
+nrecord magma_type : Type[1] ≝
  { carr:> Type;
    op: carr → carr → carr
  }.
 
-nrecord magma (A: pre_magma) : Type[1] ≝
+nrecord magma (A: magma_type) : Type[1] ≝
  { mcarr:> Ω \sup A;
    op_closed: ∀x,y. x ∈ mcarr → y ∈ mcarr → op A x y ∈ mcarr
  }.
 
-nrecord pre_magma_morphism (A,B: pre_magma) : Type ≝
+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)
  }.
 
 nrecord magma_morphism (A) (B) (Ma: magma A) (Mb: magma B) : Type ≝
- { mmmcarr:> pre_magma_morphism A B;
+ { mmmcarr:> magma_morphism_type A B;
    mmclosed: ∀x. x ∈ Ma → mmmcarr x ∈ Mb
  }.
  
-ndefinition sub_magma ≝
- λA.λM1,M2: magma A. M1 ⊆ M2.
- 
 ndefinition image: ∀A,B. (A → B) → Ω \sup A → Ω \sup B ≝
  λA,B,f,Sa. {y | ∃x. x ∈ Sa ∧ f x = y}.
 
@@ -71,4 +68,12 @@ ndefinition mm_counter_image:
          | 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 (M1 ∩ M2)
+  | #x; #y; nwhd in ⊢ (% → % → %); *; #Hx1; #Hx2; *; #Hy1; #Hy2;
+    napply (conj ????); napply (op_closed ??????); nassumption ]
 nqed.
\ No newline at end of file
-- 
2.39.2