theorem
proved
tactic proof
kernel_dynamical_time_ge_one
show as:
view Lean formalization →
formal statement (Lean)
411theorem kernel_dynamical_time_ge_one (P : KernelParams) (T_dyn : ℝ) :
412 1 ≤ kernel_dynamical_time P T_dyn := by
proof body
Tactic-mode proof.
413 unfold kernel_dynamical_time
414 have hmax_pos : 0 < max 0.01 (T_dyn / P.tau0) := by
415 apply lt_max_of_lt_left; norm_num
416 have hpow_nonneg : 0 ≤ (max 0.01 (T_dyn / P.tau0)) ^ P.alpha :=
417 Real.rpow_nonneg (le_of_lt hmax_pos) P.alpha
418 have hcorr_nonneg : 0 ≤ P.C * (max 0.01 (T_dyn / P.tau0)) ^ P.alpha :=
419 mul_nonneg P.C_nonneg hpow_nonneg
420 linarith
421
422/-- **No cumulative-time growth.** For a stationary orbit `T_dyn(t) = T_dyn`
423constant in time `t`, the dynamical-time kernel is constant in time. This
424resolves Beltracchi's concern (1): the gravitational acceleration on a
425test particle in a stable orbit does not grow as `t^α`. -/