Theorems · Theorem · functional analysis
mul_mem_ball_iff_norm
∀ {E : Type u_5} [inst : SeminormedCommGroup E] {a b : E} {r : ℝ}, a * b ∈ Metric.ball a r ↔ ‖b‖ < r- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedCommGroup
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Metric.ballstatement · cited by 735
- SeminormedCommGroupstatement and proof · cited by 191
- mul_div_cancel_leftproof · cited by 9
- mem_ball_iff_norm''proof · cited by 2
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