minor corrections and updates

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / nstream.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream.ma
index 7ba0d13eb3e641b004d6fc2598584b58015ef9d1..c5ccb7373a489400abfad21e4e23e1170713cb11 100644 (file)
--- 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/upspoon_1.ma".
+include "ground_2/lib/stream_tls.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
 definition rtmap: Type[0] ≝ stream nat.
+
+definition push: rtmap → rtmap ≝ λf. 0⨮f.
+
+interpretation "push (nstream)" 'UpSpoon f = (push f).
+
+definition next: rtmap → rtmap.
+* #n #f @(↑n⨮f)
+defined.
+
+interpretation "next (nstream)" 'UpArrow 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.