Theorems · Theorem · commutative algebra
Valuation.map_sum_le
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
{ι : Type u_7} {s : Finset ι} {f : ι → R} {g : Γ₀}, (∀ i ∈ s, v (f i) ≤ g) → v (∑ i ∈ s, f i) ≤ g- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- Valuationstatement and proof · cited by 823
- zero_leproof · cited by 382
- Finset.sum_insertproof · cited by 196
- Finset.induction_onproof · cited by 167
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Finset.forall_mem_insertproof · cited by 19
- Valuation.map_zeroproof · cited by 11
- Valuation.map_add_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.valuation_le_one_of_valuation_X_le_oneproof · cited by 2
- AddValuation.map_le_sumproof · cited by 0