Theorems · Theorem · general topology
lipschitz_with_lipschitz_const_add
∀ {β : Type u_2} [inst : PseudoMetricSpace β] [inst_1 : AddMonoid β] [inst_2 : LipschitzAdd β] (p q : β × β),
dist (p.1 + p.2) (q.1 + q.2) ≤ ↑(LipschitzAdd.C β) * dist p q- Defined in
- Mathlib.Topology.MetricSpace.Algebra
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- AddMonoidstatement and proof · cited by 2,864
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- lipschitzWith_iff_dist_le_mulproof · cited by 10
- LipschitzAddstatement and proof · cited by 6
- LipschitzAdd.Cstatement · cited by 2
- lipschitzWith_lipschitz_const_add_edistproof · cited by 1
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