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Theorems · Theorem · commutative algebra

ValuativeRel.not_vlt

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y : R}, ¬x <ᵥ y ↔ y ≤ᵥ x
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
3 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringValuativeRel
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Around this declaration

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

ValuativeRel.vle.not_vlt · cited by 2vle.not_vltValuativeRel.exists_valuation_posSubmonoid_div_valuation_posSubmonoid_eq · cited by 1ValuativeRel.exists_valua…ValuativeRel.zero_vlt_mul · cited by 0ValuativeRel.zero_vlt_mulSemiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.vlt · cited by 49ValuativeRel.vltIff.not_left · cited by 49Iff.not_leftValuativeRel.not_vle · cited by 4ValuativeRel.not_vleValuativeRel.not_vltCITED BYCITES

Cites6

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

Cited by3

Results whose statement or proof uses this declaration.