Theorems · Theorem · field theory
Subsemigroup.mem_unitBall
∀ (𝕜 : Type u_2) [inst : NonUnitalSeminormedRing 𝕜] {x : 𝕜}, x ∈ Subsemigroup.unitBall 𝕜 ↔ ‖x‖ < 1- Defined in
- Mathlib.Analysis.Normed.Field.UnitBall
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalSeminormedRing
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- Metric.ballproof · cited by 735
- Subsemigroupstatement · cited by 323
- dist_zero_rightproof · cited by 172
- NonUnitalSeminormedRingstatement and proof · cited by 44
- Subsemigroup.unitBallstatement · cited by 1
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