Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.mk_eq_div
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] (r : R) (s : ↥(ValuativeRel.posSubmonoid R)),
ValuativeRel.ValueGroupWithZero.mk r s = (ValuativeRel.valuation R) r / (ValuativeRel.valuation R) ↑s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- mul_oneproof · cited by 3,885
- Submonoidstatement · cited by 3,086
- Valuationstatement · cited by 823
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement · cited by 86
- ValuativeRel.vleproof · cited by 84
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.valuationstatement · cited by 42
- eq_div_iffproof · cited by 38
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- ValuativeRel.ValueGroupWithZero.embedding_embed_valuation_eqproof · cited by 1
- ValuativeExtension.mapValueGroupWithZero_mkproof · cited by 1
- ValuativeRel.ValueGroupWithZero.mk_eq_valuationproof · cited by 1