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[helm.git] / helm / software / matita / nlibrary / sets / setoids1.ma

diff --git a/helm/software/matita/nlibrary/sets/setoids1.ma b/helm/software/matita/nlibrary/sets/setoids1.ma
index 6d6b68743195a8acd2f86b6b4b134165d10e35dd..49d259d5dd46ddb0d7efff2f0bf532794d8589df 100644 (file)
--- a/helm/software/matita/nlibrary/sets/setoids1.ma
+++ b/helm/software/matita/nlibrary/sets/setoids1.ma
@@ -69,11 +69,41 @@ ndefinition unary_morphism1_setoid1: setoid1 → setoid1 → setoid1.
  #s; #s1; @ (unary_morphism1 s s1); @
      [ #f; #g; napply (∀a:s. f a = g a)
      | #x; #a; napply refl1
-     | #x; #y; #H; #a; napply sym1; nauto
+     | #x; #y; #H; #a; napply sym1; //
      | #x; #y; #z; #H1; #H2; #a; napply trans1; ##[##2: napply H1 | ##skip | napply H2]##]
 nqed.
 
 unification hint 0 ≔ S, T ;
  R ≟ (unary_morphism1_setoid1 S T)
 (* --------------------------------- *) ⊢
-   carr1 R ≡ unary_morphism1 S T.
\ No newline at end of file
+   carr1 R ≡ unary_morphism1 S T.
+
+ndefinition composition1 ≝
+ λo1,o2,o3:Type[1].λf:o2 → o3.λg: o1 → o2.λx.f (g x).
+ 
+interpretation "function composition" 'compose f g = (composition ??? f g).
+interpretation "function composition1" 'compose f g = (composition1 ??? f g).
+
+ndefinition comp1_unary_morphisms:
+ ∀o1,o2,o3:setoid1.
+  unary_morphism1 o2 o3 → unary_morphism1 o1 o2 →
+   unary_morphism1 o1 o3.
+#o1; #o2; #o3; #f; #g; @ (f ∘ g);
+ #a; #a'; #e; nnormalize; napply (.= †(†e)); napply #.
+nqed.
+
+unification hint 0 ≔ o1,o2,o3:setoid1,f:unary_morphism1 o2 o3,g:unary_morphism1 o1 o2;
+   R ≟ (mk_unary_morphism1 ?? (composition1 … f g)
+        (prop11 ?? (comp1_unary_morphisms o1 o2 o3 f g)))
+ (* -------------------------------------------------------------------- *) ⊢
+                              fun11 ?? R ≡ (composition1 … f g).
+                              
+ndefinition comp_binary_morphisms:
+ ∀o1,o2,o3.
+  binary_morphism1 (unary_morphism1_setoid1 o2 o3) (unary_morphism1_setoid1 o1 o2)
+   (unary_morphism1_setoid1 o1 o3).
+#o1; #o2; #o3; @
+ [ #f; #g; napply (comp1_unary_morphisms … f g) (*CSC: why not ∘?*)
+ | #a; #a'; #b; #b'; #ea; #eb; #x; nnormalize;
+   napply (.= †(eb x)); napply ea.
+nqed.