Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.inv_mk
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] (x : R) (y : ↥(ValuativeRel.posSubmonoid R))
(hx : ¬x ≤ᵥ 0), (ValuativeRel.ValueGroupWithZero.mk x y)⁻¹ = ValuativeRel.ValueGroupWithZero.mk ↑y ⟨x, hx⟩- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 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
- Submonoidstatement · cited by 3,086
- 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 · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.exists_valuation_div_valuation_eqproof · cited by 2