Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.mk_le_mk
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] (x y : R) (t s : ↥(ValuativeRel.posSubmonoid R)),
ValuativeRel.ValueGroupWithZero.mk x t ≤ ValuativeRel.ValueGroupWithZero.mk y s ↔ x * ↑s ≤ᵥ y * ↑t- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 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 · 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.ValueGroupWithZero.mk_lt_mkproof · cited by 0