strictAnti_of_hasDerivAt_neg

∀ {f f' : ℝ → ℝ}, (∀ (x : ℝ), HasDerivAt f (f' x) x) → (∀ (x : ℝ), f' x < 0) → StrictAnti f

Let f : ℝ → ℝ be a differentiable function. If f' is strictly positive, then f is a strictly monotone function.

Defined in: Mathlib.Analysis.Calculus.Deriv.MeanValue
Cited by: 0 results in Mathlib
Foundations: Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound

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