Theorems · Theorem · commutative algebra
ValuativeRel.mul_vlt_mul_iff_left
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y z : R}, 0 <ᵥ z → (x * z <ᵥ y * z ↔ x <ᵥ y)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Iff.notproof · cited by 489
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.mul_vle_mul_iff_leftproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vlt_mul_leftproof · cited by 3
- ValuativeRel.vlt_mul_right_iffproof · cited by 0