IdentityTickRefrigeratorCert

formal source

  65
  66/-! ## §2. Master certificate -/
  67
  68structure IdentityTickRefrigeratorCert where
  69  fraction_pos : 0 < coolingFraction
  70  fraction_band : (0.11 : ℝ) < coolingFraction ∧ coolingFraction < 0.13
  71  cumulative_zero : cumulativeCooling 0 = 0
  72  cumulative_succ : ∀ n, cumulativeCooling (n + 1) = cumulativeCooling n + coolingFraction
  73  cumulative_pos : ∀ {n : ℕ}, 1 ≤ n → 0 < cumulativeCooling n
  74  cumulative_strict_mono : ∀ {n m : ℕ}, n < m →
  75    cumulativeCooling n < cumulativeCooling m
  76
  77def identityTickRefrigeratorCert : IdentityTickRefrigeratorCert where
  78  fraction_pos := coolingFraction_pos
  79  fraction_band := coolingFraction_band
  80  cumulative_zero := cumulativeCooling_zero
  81  cumulative_succ := cumulativeCooling_succ
  82  cumulative_pos := @cumulativeCooling_pos
  83  cumulative_strict_mono := @cumulativeCooling_strict_mono
  84
  85/-- **REFRIGERATOR ONE-STATEMENT.** Per-cycle cooling fraction
  86`J(φ) ∈ (0.11, 0.13)`; cumulative cooling additive in cycles, strictly
  87monotonic. -/
  88theorem refrigerator_one_statement :
  89    0 < coolingFraction ∧
  90    (0.11 : ℝ) < coolingFraction ∧ coolingFraction < 0.13 ∧
  91    (∀ {n m : ℕ}, n < m → cumulativeCooling n < cumulativeCooling m) :=
  92  ⟨coolingFraction_pos, coolingFraction_band.1, coolingFraction_band.2,
  93   @cumulativeCooling_strict_mono⟩
  94
  95end
  96
  97end IdentityTickRefrigeratorSpec
  98end Engineering