lemma
proved
tactic proof
kappa_discreteness
show as:
view Lean formalization →
formal statement (Lean)
143lemma kappa_discreteness (P : SpiralField.Params) (d : ℤ) :
144 SpiralField.perTurnMultiplier { kappa := P.kappa + d }
proof body
Tactic-mode proof.
145 = SpiralField.perTurnMultiplier P * Real.rpow IndisputableMonolith.Constants.phi (d : ℝ) := by
146 -- `φ > 0` so we can use `Real.rpow_add`.
147 have hφpos : 0 < IndisputableMonolith.Constants.phi := IndisputableMonolith.Constants.phi_pos
148 -- Expand both sides and use `rpow_add` on the exponent `(κ + d)`.
149 simp [SpiralField.perTurnMultiplier, Real.rpow_add, hφpos, Int.cast_add]
150
151end SpiralLemmas
152
153end Geometry
154end Flight
155end IndisputableMonolith