Theorems · Theorem · commutative algebra
Valuation.map_add_of_distinct_val
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
{x y : R}, v x ≠ v y → v (x + y) = max (v x) (v y)- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 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.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- add_commproof · cited by 1,535
- Valuationstatement and proof · cited by 823
- lt_irreflproof · cited by 190
- add_sub_cancel_rightproof · cited by 187
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Ne.lt_or_gtproof · cited by 108
- max_ltproof · cited by 42
- max_commproof · cited by 41
- le_iff_eq_or_ltproof · cited by 20
- Valuation.map_addproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- Valuation.map_eq_of_sub_ltproof · cited by 7
- Valuation.map_add_eq_of_lt_rightproof · cited by 2
- AddValuation.map_add_of_distinct_valproof · cited by 1