Theorems · Theorem · order theory
Real.smul_iSup_of_nonneg
∀ {ι : Sort u_1} {α : Type u_2} [inst : Field α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α]
[inst_3 : MulActionWithZero α ℝ] [IsOrderedModule α ℝ] {a : α}, 0 ≤ a → ∀ (f : ι → ℝ), a • ⨆ i, f i = ⨆ i, a • f i- Defined in
- Mathlib.Data.Real.Pointwise
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Set.rangeproof · cited by 4,705
- IsStrictOrderedRingstatement and proof · cited by 2,490
- iSupstatement · cited by 2,415
- SupSet.sSupproof · cited by 954
- Set.range_compproof · cited by 223
- IsOrderedModulestatement and proof · cited by 156
- MulActionWithZerostatement and proof · cited by 79
- Real.sSup_smul_of_nonnegproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Real.mul_iSup_of_nonnegproof · cited by 5