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Theorems · Theorem · commutative algebra

ValuativeRel.not_vle

∀ {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
4 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
SemiringValuativeRel
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Around this declaration

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

ValuativeRel.not_vlt · cited by 3ValuativeRel.not_vltValuativeExtension.vlt_iff_vlt · cited by 0ValuativeExtension.vlt_if…ValuativeRel.ValueGroupWithZero.mk_lt_mk · cited by 0ValueGroupWithZero.mk_lt_…ValuativeRel.vlt.not_vle · cited by 0vlt.not_vleSemiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.vlt · cited by 49ValuativeRel.vltValuativeRel.not_vleCITED BYCITES

Cites4

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

Cited by4

Results whose statement or proof uses this declaration.