inductive unit : Set ≝ something: unit.
-inductive Prod (A,B:Set) : Set \def
+inductive Prod (A,B:Type) : Type \def
pair : A \to B \to Prod A B.
interpretation "Pair construction" 'pair 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].
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