Theorems · Theorem · commutative algebra
Valuation.map_add
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
(x y : R), v (x + y) ≤ max (v x) (v y)- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.map_add_le_max'proof · cited by 3
Cited by17
Results whose statement or proof uses this declaration.
- Valuation.map_add_ltproof · cited by 4
- Valuation.map_add_leproof · cited by 3
- Valuation.map_add_of_distinct_valproof · cited by 3
- Valuation.map_subproof · cited by 3
- Valuation.isOpen_ballproof · cited by 3
- Valuation.isOpen_closedBallproof · cited by 3
- Valued.isOpen_closedBallproof · cited by 3
- AddValuation.map_addproof · cited by 2
- Valuation.isEquiv_iff_val_eq_oneproof · cited by 2
- Valued.isOpen_ballproof · cited by 2
- Valuation.map_add_suppproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_adicAbvDefproof · cited by 1