Theorems · Theorem · functional analysis
QuotientGroup.norm_lt_iff
∀ {M : Type u_1} [inst : SeminormedCommGroup M] {S : Subgroup M} {x : M ⧸ S} {r : ℝ}, ‖x‖ < r ↔ ∃ m, ↑m = x ∧ ‖m‖ < r- Defined in
- Mathlib.Analysis.Normed.Group.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.infDist_lt_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- QuotientGroup.exists_norm_mk_ltproof · cited by 1
- QuotientGroup.nhds_one_hasBasisproof · cited by 0