Theorems · Theorem · commutative algebra
Valuation.map_sub
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Ringstatement and proof · cited by 7,463
- sub_eq_add_negproof · cited by 1,023
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.map_addproof · cited by 17
- Valuation.map_negproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Valuation.map_add_of_distinct_valproof · cited by 3
- Valuation.map_sub_of_left_eq_zeroproof · cited by 2
- AddValuation.map_subproof · cited by 0