Theorems · Theorem · functional analysis
ediam_add_le
∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] (x y : Set E), Metric.ediam (x + y) ≤ Metric.ediam x + Metric.ediam y- Defined in
- Mathlib.Analysis.Normed.Group.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Set.addstatement · cited by 338
- LE.le.trans_eqproof · cited by 328
- Metric.ediamstatement and proof · cited by 159
- Isometry.lipschitzproof · cited by 22
- LipschitzWith.lipschitzOnWithproof · cited by 16
- isometry_add_leftproof · cited by 3
- LipschitzOnWith.ediam_image2_leproof · cited by 3
- isometry_add_rightproof · cited by 2
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