Theorems · Theorem · functional analysis
AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder
∀ {p : ℝ} [hp : Fact (0 < p)] {u : AddCircle p}, IsOfFinAddOrder u → u ≠ 0 → p ≤ addOrderOf u • ‖u‖- Defined in
- Mathlib.Analysis.Normed.Group.AddCircle
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Factstatement and proof · cited by 2,726
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- mul_assocproof · cited by 1,667
- LT.lt.ne'proof · cited by 1,417
- AddSubgroup.zmultiplesstatement · cited by 493
- nsmul_eq_mulproof · cited by 369
- Fact.outproof · cited by 328
Cited by1
Results whose statement or proof uses this declaration.
- AddCircle.isAddFundamentalDomain_of_ae_ballproof · cited by 1