Theorems · Theorem · commutative algebra
ValuativeRel.ValueGroupWithZero.mk_lt_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
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringValuativeRel
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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
- Submonoidstatement · cited by 3,086
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.ValueGroupWithZerostatement · cited by 86
- ValuativeRel.vleproof · cited by 84
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.posSubmonoidstatement and proof · cited by 45
- ValuativeRel.ValueGroupWithZero.mkstatement and proof · cited by 25
- lt_iff_not_geproof · cited by 22
- ValuativeRel.not_vleproof · cited by 4
- ValuativeRel.ValueGroupWithZero.mk_le_mkproof · cited by 1
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