Theorems · Theorem · commutative algebra
ValuativeRel.mul_vle_mul_right
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y : R}, x ≤ᵥ y → ∀ (z : R), z * x ≤ᵥ z * y- Cited by
- 5 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.
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.mul_vle_mul_leftproof · cited by 6
- ValuativeRel.vle_transproof · cited by 4
- ValuativeRel.veq_mul_commproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- ValuativeRel.mul_vle_mulproof · cited by 2
- ValuativeRel.mul_vlt_mul_of_vlt_of_vleproof · cited by 0
- ValuativeRel.pow_vle_pow_of_one_vleproof · cited by 0
- ValuativeRel.pow_vle_pow_of_vle_oneproof · cited by 0
- ValuativeRel.mul_vlt_mulproof · cited by 0