ProdT was a perfect copy of Prod. Removed.

Sum is now in Type.

diff --git a/helm/software/matita/library/algebra/CoRN/SemiGroups.ma b/helm/software/matita/library/algebra/CoRN/SemiGroups.ma
index f57e7c41ab7cedfe9884c4056a19ee94898b9d6f..b57d3b2fde5f22d2a735e277df8be2f35090d085 100644 (file)
--- a/helm/software/matita/library/algebra/CoRN/SemiGroups.ma
+++ b/helm/software/matita/library/algebra/CoRN/SemiGroups.ma
@@ -269,10 +269,10 @@ definition dprod: \forall M1,M2:CSemiGroup. \forall x:ProdCSetoid (csg_crr M1) (
   \lambda M1,M2:CSemiGroup. \lambda x:ProdCSetoid (csg_crr M1) (csg_crr M2).
   \lambda y:ProdCSetoid (csg_crr M1) (csg_crr M2).
   match x with 
-    [pairT (x1: (cs_crr (csg_crr M1))) (x2: (cs_crr (csg_crr M2))) \Rightarrow 
+    [pair (x1: (cs_crr (csg_crr M1))) (x2: (cs_crr (csg_crr M2))) \Rightarrow 
      match y with 
-       [pairT (y1: (cs_crr (csg_crr M1))) (y2: (cs_crr (csg_crr M2))) \Rightarrow 
-          pairT (cs_crr (csg_crr M1)) (cs_crr (csg_crr M2))
+       [pair (y1: (cs_crr (csg_crr M1))) (y2: (cs_crr (csg_crr M2))) \Rightarrow 
+          pair (cs_crr (csg_crr M1)) (cs_crr (csg_crr M2))
 (csbf_fun ? ? ? (csg_op M1) x1 y1) (csbf_fun ? ? ? (csg_op M2) x2 y2)]].
 
 lemma dprod_strext: \forall M1,M2:CSemiGroup.

diff --git a/helm/software/matita/library/algebra/CoRN/Setoids.ma b/helm/software/matita/library/algebra/CoRN/Setoids.ma
index 982d61caf19297e62b99abb2ed35c1c98af465f3..30c8c8bd5d128ebefbfc2d212f5e7ac75f8927ac 100644 (file)
--- a/helm/software/matita/library/algebra/CoRN/Setoids.ma
+++ b/helm/software/matita/library/algebra/CoRN/Setoids.ma
@@ -215,19 +215,19 @@ qed.
 
 (* -----------------The product of setoids----------------------- *)
 
-definition prod_ap: \forall A,B : CSetoid.\forall c,d: ProdT A B. Prop \def
-\lambda A,B : CSetoid.\lambda c,d: ProdT A B.
-  ((cs_ap A (fstT A B c) (fstT A B d)) \or 
-   (cs_ap B (sndT A B c) (sndT A B d))).
-
-definition prod_eq: \forall A,B : CSetoid.\forall c,d: ProdT A B. Prop \def
-\lambda A,B : CSetoid.\lambda c,d: ProdT A B.
-  ((cs_eq A (fstT A B c) (fstT A B d)) \and 
-   (cs_eq B (sndT A B c) (sndT A B d))).
+definition prod_ap: \forall A,B : CSetoid.\forall c,d: Prod A B. Prop \def
+\lambda A,B : CSetoid.\lambda c,d: Prod A B.
+  ((cs_ap A (fst A B c) (fst A B d)) \or 
+   (cs_ap B (snd A B c) (snd A B d))).
+
+definition prod_eq: \forall A,B : CSetoid.\forall c,d: Prod A B. Prop \def
+\lambda A,B : CSetoid.\lambda c,d: Prod A B.
+  ((cs_eq A (fst A B c) (fst A B d)) \and 
+   (cs_eq B (snd A B c) (snd A B d))).
       
 
 lemma prodcsetoid_is_CSetoid: \forall A,B: CSetoid.
- is_CSetoid (ProdT A B) (prod_eq A B) (prod_ap A B).
+ is_CSetoid (Prod A B) (prod_eq A B) (prod_ap A B).
 intros.
 apply (mk_is_CSetoid ? (prod_eq A B) (prod_ap A B))
   [unfold.
@@ -301,7 +301,7 @@ qed.
 
 definition ProdCSetoid : \forall A,B: CSetoid. CSetoid \def
  \lambda A,B: CSetoid.
-  mk_CSetoid (ProdT A B) (prod_eq A B) (prod_ap A B) (prodcsetoid_is_CSetoid A B).
+  mk_CSetoid (Prod A B) (prod_eq A B) (prod_ap A B) (prodcsetoid_is_CSetoid A B).
 
 
 

diff --git a/helm/software/matita/library/datatypes/constructors.ma b/helm/software/matita/library/datatypes/constructors.ma
index 6d0a68503bb809a72c689be947ef81f38e812c89..dd2a1760b9c640c7853fafbeb33babe2d7670ad2 100644 (file)
--- a/helm/software/matita/library/datatypes/constructors.ma
+++ b/helm/software/matita/library/datatypes/constructors.ma
@@ -34,11 +34,11 @@ interpretation "Product" 'product x y =
 notation "hvbox(x break \times y)" with precedence 89
 for @{ 'product $x $y}.
 
-definition fst \def \lambda A,B:Set.\lambda p: Prod A B.
+definition fst \def \lambda A,B:Type.\lambda p: Prod A B.
 match p with
 [(pair a b) \Rightarrow a]. 
 
-definition snd \def \lambda A,B:Set.\lambda p: Prod A B.
+definition snd \def \lambda A,B:Type.\lambda p: Prod A B.
 match p with
 [(pair a b) \Rightarrow b].
 
@@ -54,25 +54,17 @@ interpretation "Second projection" 'snd x =
 notation "\snd x" with precedence 89
 for @{ 'snd $x}.
 
-theorem eq_pair_fst_snd: \forall A,B:Set.\forall p:Prod A B.
+theorem eq_pair_fst_snd: \forall A,B:Type.\forall p:Prod A B.
 p = 〈 (\fst p), (\snd p) 〉.
 intros.elim p.simplify.reflexivity.
 qed.
 
-inductive Sum (A,B:Set) : Set \def
+inductive Sum (A,B:Type) : Type \def
   inl : A \to Sum A B
 | inr : B \to Sum A B.
 
-inductive ProdT (A,B:Type) : Type \def
-pairT : A \to B \to ProdT A B.
-
-definition fstT \def \lambda A,B:Type.\lambda p: ProdT A B.
-match p with
-[(pairT a b) \Rightarrow a]. 
-
-definition sndT \def \lambda A,B:Type.\lambda p: ProdT A B.
-match p with
-[(pairT a b) \Rightarrow b].
+interpretation "Disjoint union" 'plus A B =
+ (cic:/matita/datatypes/constructors/Sum.ind#xpointer(1/1) A B).
 
 inductive option (A:Type) : Type ≝
    None : option A