Theorems · Theorem · real analysis
Real.rpow_sum_of_nonneg
∀ {ι : Type u_1} {a : ℝ}, 0 ≤ a → ∀ {s : Finset ι} {f : ι → ℝ}, (∀ x ∈ s, 0 ≤ f x) → a ^ ∑ x ∈ s, f x = ∏ x ∈ s, a ^ f x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finsetstatement and proof · cited by 13,712
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- Finset.consproof · cited by 221
- Finset.sum_nonnegproof · cited by 91
- Finset.cons_inductionproof · cited by 85
- Finset.sum_consproof · cited by 84
- Real.rpow_zeroproof · cited by 69
- Finset.prod_consproof · cited by 60
- Finset.sum_emptyproof · cited by 45
- Finset.prod_emptyproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Real.geom_mean_eq_arith_mean_weighted_iff_of_posproof · cited by 2
- Real.geom_mean_weighted_of_constantproof · cited by 1