commit by user andrea

[helm.git] / weblib / basics / types.ma

diff --git a/weblib/basics/types.ma b/weblib/basics/types.ma
index c14cc60b4bf4f32ef21f34965932982f2fafdc44..586ce31ce7bb527d251d3d1a9ddf5704f9163a2a 100644 (file)
--- a/weblib/basics/types.ma
+++ b/weblib/basics/types.ma
@@ -25,10 +25,10 @@ interpretation "Pair construction" 'pair x y = (pair ? ? x y).
 
 interpretation "Product" 'product x y = (Prod x y).
 
-definition fst ≝ λA,B.λp:A × B.
+definition fst ≝ λA,B.λp:A \ 5a title="Product" href="cic:/fakeuri.def(1)"\ 6×\ 5/a\ 6 B.
   match p with [pair a b ⇒ a]. 
 
-definition snd ≝ λA,B.λp:A × B.
+definition snd ≝ λA,B.λp:A \ 5a title="Product" href="cic:/fakeuri.def(1)"\ 6×\ 5/a\ 6 B.
   match p with [pair a b ⇒ b].
 
 interpretation "pair pi1" 'pi1 = (fst ? ?).
@@ -38,8 +38,8 @@ 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: ∀A,B.∀p:A × B.
-  p = 〈 \fst p, \snd p 〉.
+theorem eq_pair_fst_snd: ∀A,B.∀p:A \ 5a title="Product" href="cic:/fakeuri.def(1)"\ 6×\ 5/a\ 6 B.
+  p \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a title="Pair construction" href="cic:/fakeuri.def(1)"\ 6〈\ 5/a\ 6 \ 5a title="pair pi1" href="cic:/fakeuri.def(1)"\ 6\fst\ 5/a\ 6 p, \ 5a title="pair pi2" href="cic:/fakeuri.def(1)"\ 6\snd\ 5/a\ 6 p 〉.
 #A #B #p (cases p) // qed.
 
 (* sum *)
@@ -56,4 +56,6 @@ inductive option (A:Type[0]) : Type[0] ≝
 
 (* sigma *)
 inductive Sig (A:Type[0]) (f:A→Type[0]) : Type[0] ≝
-  dp: ∀a:A.(f a)→Sig A f.
\ No newline at end of file
+  dp: ∀a:A.(f a)→Sig A f.
+
+interpretation "Sigma" 'sigma x = (Sig ? x).
\ No newline at end of file