Theorems · Theorem · commutative algebra
ValuativeRel.vle_mul_cancel
∀ {R : Type u_1} {inst : Semiring R} [self : ValuativeRel R] {x y z : R}, ¬z ≤ᵥ 0 → x * z ≤ᵥ y * z → x ≤ᵥ y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- ValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.vlestatement · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vle_mul_iff_leftproof · cited by 5
- ValuativeRel.zero_vlt_mulproof · cited by 0