Theorems · Theorem · commutative algebra
ValuativeRel.mul_vlt_mul_iff_right
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y z : R}, 0 <ᵥ x → (x * y <ᵥ x * z ↔ y <ᵥ z)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- 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_rightproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vlt_mul_rightproof · cited by 2
- ValuativeRel.vlt_mul_left_iffproof · cited by 0