Theorems · Theorem · commutative algebra
AddValuation.map_lt_sum
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedAddCommMonoidWithTop Γ₀] (v : AddValuation R Γ₀)
{ι : Type u_6} {s : Finset ι} {f : ι → R} {g : Γ₀}, g ≠ ⊤ → (∀ i ∈ s, g < v (f i)) → g < v (∑ i ∈ s, f i)- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement · cited by 5,195
- AddValuationstatement and proof · cited by 96
- LinearOrderedAddCommMonoidWithTopstatement and proof · cited by 68
- Valuation.map_sum_ltproof · cited by 4
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