Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.mk_eq_zero
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] (x : R) (y : ↥(ValuativeRel.posSubmonoid R)),
ValuativeRel.ValueGroupWithZero.mk x y = 0 ↔ x ≤ᵥ 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 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.
Cites11
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
- mul_oneproof · cited by 3,885
- Submonoidstatement · cited by 3,086
- MulZeroClass.zero_mulproof · cited by 1,625
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement · cited by 86
- ValuativeRel.vlestatement and proof · cited by 84
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
- ValuativeRel.ValueGroupWithZero.soundproof · cited by 3
- ValuativeRel.ValueGroupWithZero.mk_eq_mkproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.valuation_eq_zero_iffproof · cited by 3
- ValuativeRel.ValueGroupWithZero.mk_zeroproof · cited by 1