Theorems · Theorem · commutative algebra
ValuativeRel.zero_vlt_mul
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y : R}, 0 <ᵥ x → 0 <ᵥ y → 0 <ᵥ x * y- Cited by
- 0 results in Mathlib
- Foundations
- Depth 15 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
- MulZeroClass.mul_zeroproof · cited by 2,091
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vleproof · cited by 84
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.vle_reflproof · cited by 4
- ValuativeRel.veq_mul_commproof · cited by 4
- ValuativeRel.not_vltproof · cited by 3
- Mathlib.Tactic.GCongr.AntisymmRel.leftproof · cited by 2
- ValuativeRel.veq.symmproof · cited by 2
- ValuativeRel.vle_mul_cancelproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.posSubmonoidproof · cited by 45