Theorems · Theorem · commutative algebra

Valuation.HasExtension.val_map_le_iff

∀ {R : Type u_1} {A : Type u_2} {ΓR : Type u_3} {ΓA : Type u_4} [inst : CommRing R] [inst_1 : Ring A]
  [inst_2 : LinearOrderedCommMonoidWithZero ΓR] [inst_3 : LinearOrderedCommMonoidWithZero ΓA] [inst_4 : Algebra R A]
  (vR : Valuation R ΓR) (vA : Valuation A ΓA) [vR.HasExtension vA] (x y : R),
  vA ((algebraMap R A) x) ≤ vA ((algebraMap R A) y) ↔ vR x ≤ vR y

Defined in

Mathlib.RingTheory.Valuation.Extension

Cited by

5 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZeroAlgebraValuation.HasExtension