matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_lift.ma

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  14
  15 include "ground_2/notation/functions/lift_1.ma".
  16 include "ground_2/relocation/nstream_at.ma".
  17
  18 (* RELOCATION N-STREAM ******************************************************)
  19
  20 definition push: rtmap → rtmap ≝ λf. 0@f.
  21
  22 interpretation "push (nstream)" 'Lift f = (push f).
  23
  24 definition next: rtmap → rtmap.
  25 * #a #f @(⫯a@f)
  26 qed.
  27
  28 interpretation "next (nstream)" 'Successor f = (next f).
  29
  30 (* Basic properties on push *************************************************)
  31
  32 lemma push_at_O: ∀f. @⦃0, ↑f⦄ ≡ 0.
  33 // qed.
  34
  35 lemma push_at_S: ∀f,i1,i2. @⦃i1, f⦄ ≡ i2 → @⦃⫯i1, ↑f⦄ ≡ ⫯i2.
  36 /2 width=1 by at_S1/ qed.
  37
  38 (* Basic inversion lemmas on push *******************************************)
  39
  40 lemma push_inv_at_S: ∀f,i1,i2. @⦃⫯i1, ↑f⦄ ≡ ⫯i2 → @⦃i1, f⦄ ≡ i2.
  41 /2 width=1 by at_inv_SOS/ qed-.
  42
  43 lemma injective_push: injective ? ? push.
  44 #f1 #f2 normalize #H destruct //
  45 qed-.
  46
  47 lemma discr_push_next: ∀f1,f2. ↑f1 = ⫯f2 → ⊥.
  48 #f1 * #n2 #f2 normalize #H destruct
  49 qed-.
  50
  51 lemma discr_next_push: ∀f1,f2. ⫯f1 = ↑f2 → ⊥.
  52 * #n1 #f1 #f2 normalize #H destruct
  53 qed-.
  54
  55 (* Basic properties on next *************************************************)
  56
  57 lemma next_at: ∀f,i1,i2. @⦃i1, f⦄ ≡ i2 → @⦃i1, ⫯f⦄ ≡ ⫯i2.
  58 * /2 width=1 by at_lift/
  59 qed.
  60
  61 (* Basic inversion lemmas on next *******************************************)
  62
  63 lemma next_inv_at: ∀f,i1,i2. @⦃i1, ⫯f⦄ ≡ ⫯i2 → @⦃i1, f⦄ ≡ i2.
  64 * /2 width=1 by at_inv_xSS/
  65 qed-.
  66
  67 lemma injective_next: injective ? ? next.
  68 * #a1 #f1 * #a2 #f2 normalize #H destruct //
  69 qed-.