X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground_2%2Frelocation%2Fnstream.ma;h=c852317f895c60e34fc403dd6f7c2572bc0a3620;hb=528f8ea107f689d07d060e1d31ba32bf65b4e6ba;hp=ccd8857a8a7b254f69586f516d17c1496c06842a;hpb=750305d95b8f6bb40b5be0e9dfd05d42b256f2a1;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma
index ccd8857a8..c852317f8 100644
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma
@@ -12,9 +12,86 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground_2/lib/arith.ma".
-include "ground_2/lib/streams.ma".
+include "ground_2/notation/functions/lift_1.ma".
+include "ground_2/lib/streams_tls.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
-definition nstream: Type[0] ≝ stream nat.
+definition rtmap: Type[0] ≝ stream nat.
+
+definition push: rtmap → rtmap ≝ λf. 0@f.
+
+interpretation "push (nstream)" 'Lift f = (push f).
+
+definition next: rtmap → rtmap.
+* #n #f @(⫯n@f)
+defined.
+
+interpretation "next (nstream)" 'Successor f = (next f).
+
+(* Basic properties *********************************************************)
+
+lemma push_rew: ∀f. 0@f = ↑f.
+// qed.
+
+lemma next_rew: ∀f,n. (⫯n)@f = ⫯(n@f).
+// qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma injective_push: injective ? ? push.
+#f1 #f2 normalize #H destruct //
+qed-.
+
+lemma discr_push_next: ∀f1,f2. ↑f1 = ⫯f2 → ⊥.
+#f1 * #n2 #f2 normalize #H destruct
+qed-.
+
+lemma discr_next_push: ∀f1,f2. ⫯f1 = ↑f2 → ⊥.
+* #n1 #f1 #f2 normalize #H destruct
+qed-.
+
+lemma injective_next: injective ? ? next.
+* #n1 #f1 * #n2 #f2 normalize #H destruct //
+qed-.
+
+lemma push_inv_seq_sn: ∀f,g,n. n@g = ↑f → 0 = n ∧ g = f.
+#f #g #n <push_rew #H destruct /2 width=1 by conj/
+qed-.
+
+lemma push_inv_seq_dx: ∀f,g,n. ↑f = n@g → 0 = n ∧ g = f.
+#f #g #n <push_rew #H destruct /2 width=1 by conj/
+qed-.
+
+lemma next_inv_seq_sn: ∀f,g,n. n@g = ⫯f → ∃∃m. m@g = f & ⫯m = n.
+* #m #f #g #n <next_rew #H destruct /2 width=3 by ex2_intro/
+qed-.
+
+lemma next_inv_seq_dx: ∀f,g,n. ⫯f = n@g → ∃∃m. m@g = f & ⫯m = n.
+* #m #f #g #n <next_rew #H destruct /2 width=3 by ex2_intro/
+qed-.
+
+lemma case_prop: ∀R:predicate rtmap.
+                 (∀f. R (↑f)) → (∀f. R (⫯f)) → ∀f. R f.
+#R #H1 #H2 * * //
+qed-.
+
+lemma case_type0: ∀R:rtmap→Type[0].
+                  (∀f. R (↑f)) → (∀f. R (⫯f)) → ∀f. R f.
+#R #H1 #H2 * * //
+qed-.
+
+lemma iota_push: ∀R,a,b,f. a f = case_type0 R a b (↑f).
+// qed.
+
+lemma iota_next: ∀R,a,b,f. b f = case_type0 R a b (⫯f).
+#R #a #b * //
+qed.
+
+(* Specific properties ******************************************************)
+
+lemma tl_push: ∀f. f = ↓↑f.
+// qed.
+
+lemma tl_next: ∀f. ↓f = ↓⫯f.
+* // qed.