Theorems · Theorem · commutative algebra
Valuation.IsEquiv.lt_iff_lt
∀ {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 → ∀ {x y : R}, v₁ x < v₁ y ↔ v₂ x < v₂ y- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 4 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.
Cites6
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
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.IsEquivstatement and proof · cited by 67
- le_iff_le_iff_lt_iff_ltproof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- ValuativeRel.ValueGroupWithZero.embed_strictMonoproof · cited by 4
- Valuation.IsEquiv.lt_one_iff_lt_oneproof · cited by 2
- Valuation.IsEquiv.uniformContinuous_equiv_symmproof · cited by 1
- Valuation.IsEquiv.one_lt_iff_one_ltproof · cited by 0