QuotientAddGroup.exists_norm_mk_lt

∀ {M : Type u_1} [inst : SeminormedAddCommGroup M] {S : AddSubgroup M} {ε : ℝ} (x : M ⧸ S),
  0 < ε → ∃ m, ↑m = x ∧ ‖m‖ < ‖x‖ + ε

For any x : M ⧸ S and any 0 < ε, there is m : M such that mk' S m = x and ‖m‖ < ‖x‖ + ε.

Defined in: Mathlib.Analysis.Normed.Group.Quotient
Cited by: 3 results in Mathlib
Foundations: Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: SeminormedAddCommGroup

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