Theorems · Theorem · commutative algebra
ValuativeRel.posSubmonoid_def
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] (x : R), x ∈ ValuativeRel.posSubmonoid R ↔ 0 <ᵥ x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringValuativeRel
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.
- Semiringstatement and proof · cited by 13,802
- Submonoidstatement · cited by 3,086
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vltstatement · cited by 49
- ValuativeRel.posSubmonoidstatement · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eqproof · cited by 1
- ValuativeRel.val_posSubmonoid_ne_zeroproof · cited by 0