inductive Prod (A,B:Type) : Type \def
pair : A \to B \to Prod A B.
-interpretation "Pair construction" 'pair x y =
- (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1/1) _ _ x y).
+interpretation "Pair construction" 'pair x y = (pair ? ? x y).
-interpretation "Product" 'product x y =
- (cic:/matita/datatypes/constructors/Prod.ind#xpointer(1/1) x y).
+interpretation "Product" 'product x y = (Prod x y).
definition fst \def \lambda A,B:Type.\lambda p: Prod A B.
match p with
match p with
[(pair a b) \Rightarrow b].
-interpretation "pair pi1" 'pi1 = (fst _ _).
-interpretation "pair pi2" 'pi2 = (snd _ _).
-interpretation "pair pi1" 'pi1a x = (fst _ _ x).
-interpretation "pair pi2" 'pi2a x = (snd _ _ x).
-interpretation "pair pi1" 'pi1b x y = (fst _ _ x y).
-interpretation "pair pi2" 'pi2b x y = (snd _ _ x y).
+interpretation "pair pi1" 'pi1 = (fst ? ?).
+interpretation "pair pi2" 'pi2 = (snd ? ?).
+interpretation "pair pi1" 'pi1a x = (fst ? ? x).
+interpretation "pair pi2" 'pi2a x = (snd ? ? x).
+interpretation "pair pi1" 'pi1b x y = (fst ? ? x y).
+interpretation "pair pi2" 'pi2b x y = (snd ? ? x y).
theorem eq_pair_fst_snd: \forall A,B:Type.\forall p:Prod A B.
p = 〈 \fst p, \snd p 〉.
inl : A \to Sum A B
| inr : B \to Sum A B.
-interpretation "Disjoint union" 'plus A B =
- (cic:/matita/datatypes/constructors/Sum.ind#xpointer(1/1) A B).
+interpretation "Disjoint union" 'plus A B = (Sum A B).
inductive option (A:Type) : Type ≝
None : option A