matita/matita/contribs/lambdadelta/ground_2/steps/rtc_isrt.ma

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  14
  15 include "ground_2/notation/relations/isredtype_2.ma".
  16 include "ground_2/steps/rtc.ma".
  17
  18 (* RT-TRANSITION COUNTER ****************************************************)
  19
  20 definition isrt: relation2 nat rtc ≝ λts,c.
  21                  ∃∃ri,rs. 〈ri, rs, 0, ts〉 = c.
  22
  23 interpretation "test for costrained rt-transition counter (rtc)"
  24    'IsRedType ts c = (isrt ts c).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma isr_00: 𝐑𝐓⦃0, 𝟘𝟘⦄.
  29 /2 width=3 by ex1_2_intro/ qed.
  30
  31 lemma isr_10: 𝐑𝐓⦃0, 𝟙𝟘⦄.
  32 /2 width=3 by ex1_2_intro/ qed.
  33
  34 lemma isrt_01: 𝐑𝐓⦃1, 𝟘𝟙⦄.
  35 /2 width=3 by ex1_2_intro/ qed.
  36
  37 (* Basic inversion properties ***********************************************)
  38
  39 lemma isrt_inv_00: ∀n. 𝐑𝐓⦃n, 𝟘𝟘⦄ → 0 = n.
  40 #n * #ri #rs #H destruct //
  41 qed-.
  42
  43 lemma isrt_inv_10: ∀n. 𝐑𝐓⦃n, 𝟙𝟘⦄ → 0 = n.
  44 #n * #ri #rs #H destruct //
  45 qed-.
  46
  47 lemma isrt_inv_01: ∀n. 𝐑𝐓⦃n, 𝟘𝟙⦄ → 1 = n.
  48 #n * #ri #rs #H destruct //
  49 qed-.
  50
  51 (* Main inversion properties ************************************************)
  52
  53 theorem isrt_mono: ∀n1,n2,c. 𝐑𝐓⦃n1, c⦄ → 𝐑𝐓⦃n2, c⦄ → n1 = n2.
  54 #n1 #n2 #c * #ri1 #rs1 #H1 * #ri2 #rs2 #H2 destruct //
  55 qed-.