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

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  14
  15 include "ground_2/notation/relations/istype_2.ma".
  16 include "ground_2/steps/rtc.ma".
  17
  18 (* T-TRANSITION COUNTER *****************************************************)
  19
  20 definition ist: relation2 nat rtc ≝
  21            λts,c. 〈0,0,0,ts〉 = c.
  22
  23 interpretation "test for t-transition counter (rtc)"
  24    'IsType ts c = (ist ts c).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma isr_00: 𝐓⦃0,𝟘𝟘⦄.
  29 // qed.
  30
  31 lemma ist_01: 𝐓⦃1,𝟘𝟙⦄.
  32 // qed.
  33
  34 (* Basic inversion properties ***********************************************)
  35
  36 lemma ist_inv_00: ∀n. 𝐓⦃n,𝟘𝟘⦄ → 0 = n.
  37 #n #H destruct //
  38 qed-.
  39
  40 lemma ist_inv_01: ∀n. 𝐓⦃n,𝟘𝟙⦄ → 1 = n.
  41 #n #H destruct //
  42 qed-.
  43
  44 (* Main inversion properties ************************************************)
  45
  46 theorem ist_inj: ∀n1,n2,c. 𝐓⦃n1,c⦄ → 𝐓⦃n2,c⦄ → n1 = n2.
  47 #n1 #n2 #c #H1 #H2 destruct //
  48 qed-.
  49
  50 theorem ist_mono: ∀n,c1,c2. 𝐓⦃n,c1⦄ → 𝐓⦃n,c2⦄ → c1 = c2.
  51 #n #c1 #c2 #H1 #H2 destruct //
  52 qed-.