smul_unitBall_of_pos

∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {r : ℝ},
  0 < r → r • Metric.ball 0 1 = Metric.ball 0 r

In a real normed space, the image of the unit ball under scalar multiplication by a positive constant r is the ball of radius r.

Defined in: Mathlib.Analysis.Normed.Module.Ball.Pointwise
Cited by: 2 results in Mathlib
Foundations: Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedAddCommGroup NormedSpace

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