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Theorems · Theorem · commutative algebra

ValuativeRel.mul_vle_mul

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x x' y y' : R}, x ≤ᵥ y → x' ≤ᵥ y' → x * x' ≤ᵥ y * y'
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
SemiringValuativeRel
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ValuativeRel.pow_vle_pow · cited by 2ValuativeRel.pow_vle_powValuativeRel.mul_veq_mul · cited by 2ValuativeRel.mul_veq_mulSemiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.mul_vle_mul_left · cited by 6ValuativeRel.mul_vle_mul_…ValuativeRel.mul_vle_mul_right · cited by 5ValuativeRel.mul_vle_mul_…ValuativeRel.vle.trans · cited by 4vle.transValuativeRel.mul_vle_mulCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.