theorem
proved
rsSpectrum_pairwise_lt
show as:
view math explainer →
open explainer
Generate a durable explainer page for this declaration.
open lean source
IndisputableMonolith.CrossDomain.CardinalitySpectrum on GitHub at line 113.
browse module
All declarations in this module, on Recognition.
explainer page
depends on
used by
formal source
110theorem rsSpectrum_length : rsSpectrum.length = 20 := by decide
111
112/-- The spectrum is strictly increasing (pairwise). -/
113theorem rsSpectrum_pairwise_lt : rsSpectrum.Pairwise (· < ·) := by decide
114
115/-- All RS spectrum members are ≤ 3125 = D⁵. -/
116theorem rsSpectrum_bounded : ∀ n ∈ rsSpectrum, n ≤ 3125 := by
117 decide
118
119structure CardinalitySpectrumCert where
120 Dspatial_is_3 : Dspatial = 3
121 Dconfig_is_5 : Dconfig = 5
122 gap_as_D : gap45 = Dspatial^2 * Dconfig
123 eightTick_as_D : eightTick = 2 ^ Dspatial
124 cubeFaces_as_D : cubeFaces = twoFace * Dspatial
125 full_turn : (360 : ℕ) = eightTick * gap45
126 choose_central : (70 : ℕ) = Nat.choose 8 4
127 D_cubed : (125 : ℕ) = Dconfig^3
128 D_fifth : (3125 : ℕ) = Dconfig^5
129 spectrum_length : rsSpectrum.length = 20
130 spectrum_pairwise : rsSpectrum.Pairwise (· < ·)
131 spectrum_bounded : ∀ n ∈ rsSpectrum, n ≤ 3125
132
133def cardinalitySpectrumCert : CardinalitySpectrumCert where
134 Dspatial_is_3 := rfl
135 Dconfig_is_5 := rfl
136 gap_as_D := gap45_eq
137 eightTick_as_D := eightTick_eq
138 cubeFaces_as_D := cubeFaces_eq
139 full_turn := threeSixty_is_tick_gap
140 choose_central := seventy_is_choose_8_4
141 D_cubed := oneTwentyFive_is_Dcubed
142 D_fifth := threeOne25_is_D_fifth
143 spectrum_length := rsSpectrum_length