[Merged by Bors] - feat: forward-port PR 18990#4328
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Forward-port of leanprover-community/mathlib3#18990 Original title: feat(analysis/normed_space/basic): scaling a set scales its diameter, translating it leaves it unchanged
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Forward-port of leanprover-community/mathlib3#18990 Original title: feat(analysis/normed_space/basic): scaling a set scales its diameter, translating it leaves it unchanged
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| /-- A variant of `le_inv_smul_iff` that holds for `ennreal`. -/ | ||
| protected theorem le_inv_smul_iff {a b : ℝ≥0∞} {r : ℝ≥0} (hr₀ : r ≠ 0) : a ≤ r⁻¹ • b ↔ r • a ≤ b := | ||
| by simpa [hr₀, ENNReal.smul_def] using (mul_le_iff_le_inv (coe_ne_zero.mpr hr₀) coe_ne_top).symm | ||
| #align ennreal.le_inv_smul_iff ENNReal.le_inv_smul_iff | ||
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| /-- A variant of `inv_smul_le_iff` that holds for `ennreal`. -/ |
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ennreal should be ENNReal, right?
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Forward-port of leanprover-community/mathlib3#18990
Original title:
feat(analysis/normed_space/basic): scaling a set scales its diameter, translating it leaves it unchanged