Theorems · Theorem · functional analysis
QuotientGroup.le_norm_iff
∀ {M : Type u_1} [inst : SeminormedCommGroup M] {S : Subgroup M} {x : M ⧸ S} {r : ℝ},
r ≤ ‖x‖ ↔ ∀ (m : M), ↑m = x → r ≤ ‖m‖- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- PseudoMetricSpaceproof · cited by 1,550
- QuotientGroup.mkstatement and proof · cited by 196
- SeminormedCommGroupstatement and proof · cited by 191
- dist_oneproof · cited by 5
- Metric.le_infDistproof · cited by 3
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