Theorems · Definition · commutative algebra
Valuation.IsEquiv
{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] → Valuation R Γ₀ → Valuation R Γ'₀ → PropTwo valuations on R are defined to be equivalent if they induce the same preorder on R.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 67 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
Cited by75
Results whose statement or proof uses this declaration.
- Valuation.IsEquiv.eq_zerostatement and proof · cited by 11
- Valuation.IsEquiv.orderMonoidIsostatement and proof · cited by 8
- AddValuation.IsEquivproof · cited by 8
- Valuation.IsEquiv.eq_iffstatement and proof · cited by 7
- Valuation.IsEquiv.symmstatement and proof · cited by 7
- ValuativeRel.isEquivstatement · cited by 6
- Valuation.IsEquiv.eq_one_iff_eq_onestatement and proof · cited by 5
- Valuation.isEquiv_iff_val_le_onestatement · cited by 4
- Valuation.IsEquiv.lt_iff_ltstatement and proof · cited by 4
- Valuation.IsEquiv.ofClass_eq_zerostatement and proof · cited by 4
- Valuation.IsEquiv.orderRingIsostatement and proof · cited by 4
- Valuation.IsEquiv.reflstatement · cited by 4