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Theorems · Theorem · functional analysis

edist_smul_le

∀ {α : Type u_1} {β : Type u_2} [inst : SeminormedAddGroup α] [inst_1 : SeminormedAddGroup β]
  [inst_2 : SMulZeroClass α β] [IsBoundedSMul α β] (s : α) (x y : β), edist (s • x) (s • y) ≤ ‖s‖₊ • edist x y
Defined in
Mathlib.Analysis.Normed.MulAction
Cited by
1 results in Mathlib
Foundations
Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddGroupSeminormedAddGroupSMulZeroClassIsBoundedSMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HolderWith.smul · cited by 2HolderWith.smulENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealNNNorm.nnnorm · cited by 952NNNorm.nnnormEDist.edist · cited by 735EDist.edistSeminormedAddGroup · cited by 331SeminormedAddGroupIsBoundedSMul · cited by 329IsBoundedSMulSMulZeroClass · cited by 213SMulZeroClasslipschitzWith_smul · cited by 5lipschitzWith_smuledist_smul_leCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.