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theorem proved tactic proof

kernel_pos

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formal statement (Lean)

  93theorem kernel_pos (P : KernelParams) (k a : ℝ) : 0 < kernel P k a := by

proof body

Tactic-mode proof.

  94  unfold kernel
  95  have hmax_pos : 0 < max 0.01 (a / (k * P.tau0)) := by
  96    apply lt_max_of_lt_left
  97    norm_num
  98  have hpow_nonneg : 0 ≤ (max 0.01 (a / (k * P.tau0))) ^ P.alpha :=
  99    Real.rpow_nonneg (le_of_lt hmax_pos) P.alpha
 100  have hcorr_nonneg : 0 ≤ P.C * (max 0.01 (a / (k * P.tau0))) ^ P.alpha :=
 101    mul_nonneg P.C_nonneg hpow_nonneg
 102  linarith
 103
 104/-- Kernel is at least 1. -/

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