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Theorems · Theorem · commutative algebra

ValuativeRel.vle.not_vlt

∀ {R : Type u_1} [inst : Semiring R] [inst_1 : ValuativeRel R] {x y : R}, y ≤ᵥ x → ¬x <ᵥ y

Alias of the reverse direction of ValuativeRel.not_vlt.

Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringValuativeRel
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ValuativeRel.not_vgt_of_veq · cited by 1ValuativeRel.not_vgt_of_v…ValuativeRel.not_vlt_of_veq · cited by 1ValuativeRel.not_vlt_of_v…Semiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.vlt · cited by 49ValuativeRel.vltValuativeRel.not_vlt · cited by 3ValuativeRel.not_vltvle.not_vltCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.