- ground_2: relocation with nstream is now based on two basic functions (push and...

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_lift.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_lift.ma
index e98d8bee1f98515be0b45362e7b3f5d5f9330038..4e2f20bf68dc738a0ba30784e4363673a18fc046 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_lift.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_lift.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "ground_2/notation/functions/lift_1.ma".
-include "ground_2/relocation/nstream_at.ma".
+include "ground_2/relocation/nstream.ma".
 
 (* RELOCATION N-STREAM ******************************************************)
 
@@ -22,23 +22,23 @@ definition push: rtmap → rtmap ≝ λf. 0@f.
 interpretation "push (nstream)" 'Lift f = (push f).
 
 definition next: rtmap → rtmap.
-* #a #f @(⫯a@f)
+* #n #f @(⫯n@f)
 qed.
 
 interpretation "next (nstream)" 'Successor f = (next f).
 
-(* Basic properties on push *************************************************)
+(* Basic properties *********************************************************)
 
-lemma push_at_O: ∀f. @⦃0, ↑f⦄ ≡ 0.
+lemma push_rew: ∀f. ↑f = 0@f.
 // qed.
 
-lemma push_at_S: ∀f,i1,i2. @⦃i1, f⦄ ≡ i2 → @⦃⫯i1, ↑f⦄ ≡ ⫯i2.
-/2 width=1 by at_S1/ qed.
+lemma next_rew: ∀f,n. ⫯(n@f) = (⫯n)@f.
+// qed.
 
-(* Basic inversion lemmas on push *******************************************)
+lemma next_rew_sn: ∀f,n1,n2. n1 = ⫯n2 → n1@f = ⫯(n2@f).
+// qed.
 
-lemma push_inv_at_S: ∀f,i1,i2. @⦃⫯i1, ↑f⦄ ≡ ⫯i2 → @⦃i1, f⦄ ≡ i2.
-/2 width=1 by at_inv_SOS/ qed-.
+(* Basic inversion lemmas ***************************************************)
 
 lemma injective_push: injective ? ? push.
 #f1 #f2 normalize #H destruct //
@@ -52,18 +52,22 @@ lemma discr_next_push: ∀f1,f2. ⫯f1 = ↑f2 → ⊥.
 * #n1 #f1 #f2 normalize #H destruct
 qed-.
 
-(* Basic properties on next *************************************************)
+lemma injective_next: injective ? ? next.
+* #n1 #f1 * #n2 #f2 normalize #H destruct //
+qed-.
 
-lemma next_at: ∀f,i1,i2. @⦃i1, f⦄ ≡ i2 → @⦃i1, ⫯f⦄ ≡ ⫯i2.
-* /2 width=1 by at_lift/
-qed.
+lemma push_inv_seq_sn: ∀f,g,n. n@g = ↑f → n = 0 ∧ g = f.
+#f #g #n >push_rew #H destruct /2 width=1 by conj/
+qed-.
 
-(* Basic inversion lemmas on next *******************************************)
+lemma push_inv_seq_dx: ∀f,g,n. ↑f = n@g → n = 0 ∧ g = f.
+#f #g #n >push_rew #H destruct /2 width=1 by conj/
+qed-.
 
-lemma next_inv_at: ∀f,i1,i2. @⦃i1, ⫯f⦄ ≡ ⫯i2 → @⦃i1, f⦄ ≡ i2.
-* /2 width=1 by at_inv_xSS/
+lemma next_inv_seq_sn: ∀f,g,n. n@g = ⫯f → ∃∃m. n = ⫯m & f = m@g.
+* #m #f #g #n >next_rew #H destruct /2 width=3 by ex2_intro/
 qed-.
 
-lemma injective_next: injective ? ? next.
-* #a1 #f1 * #a2 #f2 normalize #H destruct //
+lemma next_inv_seq_dx: ∀f,g,n. ⫯f = n@g → ∃∃m. n = ⫯m & f = m@g.
+* #m #f #g #n >next_rew #H destruct /2 width=3 by ex2_intro/
 qed-.