Theorems · Theorem · commutative algebra
ValuativeRel.mul_vle_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
- 5 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SemiringValuativeRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 84
- ValuativeRel.vltstatement and proof · cited by 49
- ValuativeRel.mul_vle_mul_leftproof · cited by 6
- ValuativeRel.vle_mul_cancelproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vlt_mul_iff_leftproof · cited by 2
- ValuativeRel.mul_vle_mul_iff_rightproof · cited by 2
- ValuativeRel.div_vle_iffproof · cited by 1
- ValuativeRel.vle_div_iffproof · cited by 1
- ValuativeRel.vle_mul_right_iffproof · cited by 0