Theorems · Theorem · commutative algebra
Valuation.IsEquiv.eq_iff
∀ {R : Type u_3} {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀]
[inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] {v₁ : Valuation R Γ₀} {v₂ : Valuation R Γ'₀},
v₁.IsEquiv v₂ → ∀ {r s : R}, v₁ r = v₁ s ↔ v₂ r = v₂ s- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 24 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.IsEquivstatement and proof · cited by 67
Cited by7
Results whose statement or proof uses this declaration.
- Valuation.IsEquiv.eq_zeroproof · cited by 11
- Valuation.IsEquiv.eq_one_iff_eq_oneproof · cited by 5
- Valuation.IsEquiv.valueGroup₀Fun_specproof · cited by 3
- ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRelproof · cited by 2
- AddValuation.IsEquiv.val_eqproof · cited by 0
- Valuation.IsEquiv.val_eqproof · cited by 0
- Valuation.HasExtension.val_map_eq_iffproof · cited by 0