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Theorems · Theorem · general topology

isometry_mul_left

∀ {M : Type u} [inst : Mul M] [inst_1 : PseudoEMetricSpace M] [IsIsometricSMul M M] (a : M), Isometry fun x => a * x
Defined in
Mathlib.Topology.MetricSpace.IsometricSMul
Cited by
3 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MulPseudoEMetricSpaceIsIsometricSMul
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Around this declaration

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

edist_mul_left · cited by 2edist_mul_leftediam_mul_le · cited by 0ediam_mul_leBornology.IsBounded.of_mul · cited by 0IsBounded.of_mulPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceIsometry · cited by 230IsometryIsIsometricSMul · cited by 74IsIsometricSMulIsIsometricSMul.isometry_smul · cited by 10IsIsometricSMul.isometry_…isometry_mul_leftCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.