update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / stream_hdtl.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl.ma b/matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl.ma
index b29772d320fca59ef849ff2a0ff4bf28c713ac31..468f306de0bbcbd4429b6a4607b69779e0a31e8e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/stream_hdtl.ma
@@ -12,28 +12,39 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/notation/functions/downspoon_2.ma".
-include "ground/lib/stream_eq.ma".
-include "ground/lib/arith.ma".
+include "ground/notation/functions/downharpoonleft_2.ma".
+include "ground/notation/functions/downharpoonright_2.ma".
+include "ground/lib/stream.ma".
 
-(* STREAMS ******************************************************************)
+(* HEAD AND TAIL FOR STREAMS ************************************************)
 
-definition hd (A:Type[0]): stream A → A ≝
-              λt. match t with [ seq a _ ⇒ a ].
+definition stream_hd (A:Type[0]): stream A → A.
+#A * #a #_ @a
+defined.
 
-definition tl (A:Type[0]): stream A → stream A ≝
-              λt. match t with [ seq _ t ⇒ t ].
+interpretation
+  "head (streams)"
+  'DownHarpoonLeft A t = (stream_hd A t).
 
-interpretation "tail (stream)" 'DownSpoon A t = (tl A t).
+definition stream_tl (A:Type[0]): stream A → stream A.
+#A * #_ #t @t
+defined.
 
-(* basic properties *********************************************************)
+interpretation
+  "tail (streams)"
+  'DownHarpoonRight A t = (stream_tl A t).
 
-lemma hd_rew (A) (a) (t): a = hd A (a⨮t).
+(* Basic constructions ******************************************************)
+
+lemma stream_hd_cons (A) (a) (t):
+      a = ⇃{A}(a⨮t).
 // qed.
 
-lemma tl_rew (A) (a) (t): t = tl A (a⨮t).
+lemma stream_tl_cons (A) (a) (t):
+      t = ⇂{A}(a⨮t).
 // qed.
 
-lemma eq_stream_split (A) (t): (hd … t) ⨮ ⫰t ≗{A} t.
+lemma stream_split_tl (A) (t):
+      ⇃{A}t ⨮ ⇂t = t.
 #A * //
 qed.