Theorems · Theorem · commutative algebra
ValuativeRel.mul_vlt_mul_left
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y z : R}, 0 <ᵥ z → x <ᵥ y → x * z <ᵥ y * zAlias of the reverse direction of ValuativeRel.mul_vlt_mul_iff_left.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- ValuativeRelstatement and proof · cited by 241
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.mul_vlt_mul_iff_leftproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ValuativeRel.vlt_mul_rightproof · cited by 0
- ValuativeRel.mul_vlt_mul_of_vlt_of_vleproof · cited by 0
- ValuativeRel.mul_vlt_mulproof · cited by 0