Theorems · Theorem · commutative algebra
ValuativeRel.exists_valuation_div_valuation_eq
∀ {R : Type u_2} [inst : Ring R] [inst_1 : ValuativeRel R] (γ : ValuativeRel.ValueGroupWithZero R),
∃ a b, (ValuativeRel.valuation R) a / (ValuativeRel.valuation R) ↑b = γ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 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.
Cites16
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
- one_mulproof · cited by 2,841
- Valuationstatement · cited by 823
- div_eq_mul_invproof · cited by 715
- Subtype.propproof · cited by 505
- ValuativeRelstatement and proof · cited by 241
- Subtype.coe_etaproof · cited by 110
- ValuativeRel.ValueGroupWithZerostatement and proof · cited by 86
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.ValueGroupWithZero.embed_strictMonoproof · cited by 4
- ValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eqproof · cited by 1