Theorems · Theorem · functional analysis
dist_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), dist (s • x) (s • y) ≤ ‖s‖ * dist x y- Defined in
- Mathlib.Analysis.Normed.MulAction
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- add_zeroproof · cited by 2,707
- Dist.diststatement · cited by 1,539
- SeminormedAddGroupstatement and proof · cited by 331
- IsBoundedSMulstatement and proof · cited by 329
- SMulZeroClassstatement and proof · cited by 213
- norm_negproof · cited by 190
- dist_eq_norm_neg_addproof · cited by 46
- dist_smul_pairproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- lipschitzWith_smulproof · cited by 5
- nndist_smul_leproof · cited by 0