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theorem proved term proof

costFamily_comp_powerMap

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formal statement (Lean)

 145theorem costFamily_comp_powerMap (κ α : ℝ) {x : ℝ} (hx : 0 < x) :
 146    costFamily κ (powerMap α x) = costFamily (α * κ) x := by

proof body

Term-mode proof.

 147  unfold costFamily powerMap
 148  rw [← Real.rpow_mul (le_of_lt hx) α κ, ← Real.rpow_mul (le_of_lt hx) α (-κ)]
 149  rw [mul_neg]
 150
 151/-- The `κ`-family is even in the parameter. -/

used by (2)

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depends on (6)

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