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theorem proved tactic proof

kernel_dynamical_time_pos

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formal statement (Lean)

 399theorem kernel_dynamical_time_pos (P : KernelParams) (T_dyn : ℝ) :
 400    0 < kernel_dynamical_time P T_dyn := by

proof body

Tactic-mode proof.

 401  unfold kernel_dynamical_time
 402  have hmax_pos : 0 < max 0.01 (T_dyn / P.tau0) := by
 403    apply lt_max_of_lt_left; norm_num
 404  have hpow_nonneg : 0 ≤ (max 0.01 (T_dyn / P.tau0)) ^ P.alpha :=
 405    Real.rpow_nonneg (le_of_lt hmax_pos) P.alpha
 406  have hcorr_nonneg : 0 ≤ P.C * (max 0.01 (T_dyn / P.tau0)) ^ P.alpha :=
 407    mul_nonneg P.C_nonneg hpow_nonneg
 408  linarith
 409
 410/-- The dynamical-time kernel is at least 1. -/

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