matita/matita/contribs/lambdadelta/ground/counters/rtc_ist.ma

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  14
  15 include "ground/notation/relations/ist_2.ma".
  16 include "ground/counters/rtc.ma".
  17
  18 (* T-TRANSITION COUNTERS ****************************************************)
  19
  20 definition rtc_ist: relation2 nat rtc ≝
  21            λts,c. 〈𝟎,𝟎,𝟎,ts〉 = c.
  22
  23 interpretation
  24   "t-transition counters (rtc)"
  25   'IsT ts c = (rtc_ist ts c).
  26
  27 (* Basic constructions ******************************************************)
  28
  29 lemma rtc_ist_zz: 𝐓❪𝟎,𝟘𝟘❫.
  30 // qed.
  31
  32 lemma rtc_ist_zu: 𝐓❪𝟏,𝟘𝟙❫.
  33 // qed.
  34
  35 (* Basic inversions *********************************************************)
  36
  37 lemma rtc_ist_inv_zz (n): 𝐓❪n,𝟘𝟘❫ → 𝟎 = n.
  38 #n #H destruct //
  39 qed-.
  40
  41 lemma rtc_ist_inv_zu (n): 𝐓❪n,𝟘𝟙❫ → ninj (𝟏) = n.
  42 #n #H destruct //
  43 qed-.
  44
  45 lemma rtc_ist_inv_uz (n): 𝐓❪n,𝟙𝟘❫ → ⊥.
  46 #h #H destruct
  47 qed-.
  48
  49 (* Main inversions **********************************************************)
  50
  51 theorem rtc_ist_inj (n1) (n2) (c): 𝐓❪n1,c❫ → 𝐓❪n2,c❫ → n1 = n2.
  52 #n1 #n2 #c #H1 #H2 destruct //
  53 qed-.
  54
  55 theorem rtc_ist_mono (n) (c1) (c2): 𝐓❪n,c1❫ → 𝐓❪n,c2❫ → c1 = c2.
  56 #n #c1 #c2 #H1 #H2 destruct //
  57 qed-.