Theorems · Theorem · commutative algebra
Valuation.apply_posSubmonoid_ne_zero
∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_2} [inst_2 : LinearOrderedCommMonoidWithZero Γ₀]
(v : Valuation R Γ₀) [v.Compatible] (x : ↥(ValuativeRel.posSubmonoid R)), v ↑x ≠ 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Submonoidstatement · cited by 3,086
- Valuationstatement and proof · cited by 823
- ValuativeRelstatement and proof · cited by 241
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.Compatiblestatement and proof · cited by 71
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.valuationproof · cited by 42
- Valuation.IsEquiv.eq_zeroproof · cited by 11
- ValuativeRel.isEquivproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.apply_posSubmonoid_posproof · cited by 0