Theorems · Theorem · commutative algebra
ValuativeRel.isNontrivial_iff_isNontrivial
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_3} [inst_2 : LinearOrderedCommMonoidWithZero Γ₀]
(v : Valuation R Γ₀) [v.Compatible], ValuativeRel.IsNontrivial R ↔ v.IsNontrivial- Cited by
- 1 results in Mathlib
- Foundations
- Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- map_zeroproof · cited by 1,614
- Valuationstatement and proof · cited by 823
- ValuativeRelstatement and proof · cited by 241
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- ValuativeRel.ValueGroupWithZeroproof · cited by 86
- Valuation.Compatiblestatement and proof · cited by 71
- Iff.neproof · cited by 52
- ValuativeRel.posSubmonoidproof · cited by 45
- ValuativeRel.valuationproof · cited by 42
- Valuation.IsNontrivialstatement and proof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.isNontrivial_of_rankOneproof · cited by 0