Theorems · Definition · commutative algebra
ValuativeRel.posSubmonoid
(R : Type u_1) → [inst : Semiring R] → [ValuativeRel R] → Submonoid R
The submonoid of elements x : R whose valuation is positive.
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 16 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.
Cites7
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
- Set.ofPredproof · cited by 6,101
- Submonoidstatement · cited by 3,086
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vltproof · cited by 49
- ValuativeRel.zero_vlt_mulproof · cited by 0
- ValuativeRel.zero_vlt_oneproof · cited by 0
Cited by51
Results whose statement or proof uses this declaration.
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
- ValuativeRel.ValueGroupWithZero.embedproof · cited by 7
- ValuativeRel.ValueGroupWithZero.indstatement and proof · cited by 6
- ValuativeRel.ValueGroupWithZero.liftstatement and proof · cited by 6
- ValuativeRel.ValueGroupWithZero.embed_strictMonoproof · cited by 4
- ValuativeExtension.mapPosSubmonoidstatement and proof · cited by 4
- ValuativeRel.ValueGroupWithZero.mk_eq_divstatement and proof · cited by 3
- ValuativeRel.ValueGroupWithZero.soundstatement and proof · cited by 3
- ValuativeRel.exists_valuation_div_valuation_eqstatement and proof · cited by 2
- ValuativeRel.posSubmonoid_defstatement · cited by 2
- ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRelproof · cited by 2
- ValuativeRel.ValueGroupWithZero.mk_eq_zerostatement and proof · cited by 2