Theorems · Theorem · functional analysis
AddCircle.norm_coe_eq_abs_iff
∀ (p : ℝ) {x : ℝ}, p ≠ 0 → (‖↑x‖ = |x| ↔ |x| ≤ |p| / 2)- Defined in
- Mathlib.Analysis.Normed.Group.AddCircle
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites31
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
- mul_oneproof · cited by 3,885
- AddSubgroupstatement · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- LT.lt.leproof · cited by 2,189
- absstatement and proof · cited by 1,814
- MulZeroClass.zero_mulproof · cited by 1,625
- eq_or_neproof · cited by 1,117
- sub_zeroproof · cited by 938
- mul_negproof · cited by 590
- AddSubgroup.zmultiplesstatement · cited by 493
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