Theorems · Theorem · general topology
IsIsometricSMul.isometry_smul
∀ {M : Type u} (X : Type w) {inst : PseudoEMetricSpace X} {inst_1 : SMul M X} [self : IsIsometricSMul M X] (c : M),
Isometry fun x => c • x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsIsometricSMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Isometrystatement · cited by 230
- IsIsometricSMulstatement and proof · cited by 74
Cited by10
Results whose statement or proof uses this declaration.
- isometry_mul_leftproof · cited by 3
- dist_smulproof · cited by 2
- nndist_smulproof · cited by 2
- isometry_mul_rightproof · cited by 2
- Bornology.IsBounded.smulproof · cited by 1
- Metric.infEDist_smulproof · cited by 1
- diam_smulproof · cited by 0
- edist_smul_leftproof · cited by 0
- ediam_smulproof · cited by 0
- MeasureTheory.hausdorffMeasure_smulproof · cited by 0