Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.mk_eq_valuation
∀ {K : Type u_3} [inst : DivisionRing K] [inst_1 : ValuativeRel K] (x : K) (y : ↥(ValuativeRel.posSubmonoid K)),
ValuativeRel.ValueGroupWithZero.mk x y = (ValuativeRel.valuation K) (x / ↑y)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingValuativeRel
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 and proof · cited by 62,936
- Submonoidstatement · cited by 3,086
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement · cited by 823
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement and proof · cited by 86
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.valuationstatement and proof · cited by 42
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
- ValuativeRel.ValueGroupWithZero.mk_eq_divproof · cited by 3
- Valuation.map_divproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.valuation_surjectiveproof · cited by 1