Theorems · Theorem · commutative algebra
Valuation.isEquiv_iff_val_le_one
∀ {K : Type u_1} [inst : DivisionRing K] {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst_1 : LinearOrderedCommGroupWithZero Γ₀]
[inst_2 : LinearOrderedCommGroupWithZero Γ'₀] {v : Valuation K Γ₀} {v' : Valuation K Γ'₀},
v.IsEquiv v' ↔ ∀ {x : K}, v x ≤ 1 ↔ v' x ≤ 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 47 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 · cited by 62,936
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.IsEquivstatement · cited by 67
- Valuation.isEquiv_of_val_le_oneproof · cited by 3
- Valuation.IsEquiv.le_one_iff_le_oneproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.isEquiv_valuation_valuationSubringproof · cited by 2
- RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_oneproof · cited by 1
- Valuation.HasExtension.ofComapIntegerproof · cited by 0
- Valuation.isEquiv_tfaeproof · cited by 0