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: nstream → nstream ≝ λt. 0@t.
  21
  22 interpretation "push (nstream)" 'Lift t = (push t).
  23
  24 definition next: nstream → nstream.
  25 * #a #t @(⫯a@t)
  26 qed.
  27
  28 interpretation "next (nstream)" 'Successor t = (next t).
  29
  30 (* Basic properties on push *************************************************)
  31
  32 lemma push_at_O: ∀t. @⦃0, ↑t⦄ ≡ 0.
  33 // qed.
  34
  35 lemma push_at_S: ∀t,i1,i2. @⦃i1, t⦄ ≡ i2 → @⦃⫯i1, ↑t⦄ ≡ ⫯i2.
  36 /2 width=1 by at_S1/ qed.
  37
  38 (* Basic inversion lemmas on push *******************************************)
  39
  40 lemma push_inv_at_S: ∀t,i1,i2. @⦃⫯i1, ↑t⦄ ≡ ⫯i2 → @⦃i1, t⦄ ≡ i2.
  41 /2 width=1 by at_inv_SOS/ qed-.
  42
  43 lemma injective_push: injective ? ? push.
  44 #t1 #t2 normalize #H destruct //
  45 qed-.
  46
  47 (* Basic properties on next *************************************************)
  48
  49 lemma next_at: ∀t,i1,i2. @⦃i1, t⦄ ≡ i2 → @⦃i1, ⫯t⦄ ≡ ⫯i2.
  50 * /2 width=1 by at_lift/
  51 qed.
  52
  53 (* Basic inversion lemmas on next *******************************************)
  54
  55 lemma next_inv_at: ∀t,i1,i2. @⦃i1, ⫯t⦄ ≡ ⫯i2 → @⦃i1, t⦄ ≡ i2.
  56 * /2 width=1 by at_inv_xSS/
  57 qed-.
  58
  59 lemma injective_next: injective ? ? next.
  60 * #a1 #t1 * #a2 #t2 normalize #H destruct //
  61 qed-.