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Theorems · Theorem · commutative algebra

ValuativeRel.zero_vle

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] (x : R), 0 ≤ᵥ x
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
1 results in Mathlib
Foundations
Depth 13 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.mul_vlt_mul · cited by 0ValuativeRel.mul_vlt_mulSemiring · cited by 13802Semiringone_mul · cited by 2841one_mulMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_mulValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.mul_vle_mul_left · cited by 6ValuativeRel.mul_vle_mul_…ValuativeRel.vle_total · cited by 4ValuativeRel.vle_totalValuativeRel.not_vle_one_zero · cited by 2ValuativeRel.not_vle_one_…ValuativeRel.zero_vleCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.