Theorems · Theorem · commutative algebra
ENNReal.smul_top
∀ {R : Type u_1} [inst : Semiring R] [IsDomain R] [inst_2 : Module R ENNReal] [IsScalarTower R ENNReal ENNReal]
[Module.IsTorsionFree R ENNReal] [inst_5 : DecidableEq R] (c : R), c • ⊤ = if c = 0 then 0 else ⊤- Defined in
- Mathlib.Data.ENNReal.Action
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- IsScalarTowerstatement and proof · cited by 3,896
- IsDomainstatement and proof · cited by 2,196
- one_ne_zeroproof · cited by 885
- Module.IsTorsionFreestatement and proof · cited by 600
- smul_one_mulproof · cited by 15
- ENNReal.mul_top'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.nnreal_smul_ne_top_iffproof · cited by 1
- MeasureTheory.Measure.euclideanHausdorffMeasure_zero_or_topproof · cited by 0
- MeasureTheory.smul_extendproof · cited by 0