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theorem proved tactic proof

kernel_perturbation_pos

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formal statement (Lean)

 282theorem kernel_perturbation_pos (P : KernelParams) (k_min k a : ℝ) :
 283    0 < kernel_perturbation P k_min k a := by

proof body

Tactic-mode proof.

 284  unfold kernel_perturbation
 285  have hmax_pos : 0 < max 0.01 (a / (max k_min k * P.tau0)) := by
 286    apply lt_max_of_lt_left; norm_num
 287  have hpow_nonneg : 0 ≤ (max 0.01 (a / (max k_min k * P.tau0))) ^ P.alpha :=
 288    Real.rpow_nonneg (le_of_lt hmax_pos) P.alpha
 289  have hcorr_nonneg : 0 ≤ P.C * (max 0.01 (a / (max k_min k * P.tau0))) ^ P.alpha :=
 290    mul_nonneg P.C_nonneg hpow_nonneg
 291  linarith
 292
 293/-- The perturbation kernel is at least 1. -/

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