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Theorems · Theorem · commutative algebra

ValuativeRel.not_vgt_of_veq

∀ {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
1 results in Mathlib
Foundations
Depth 16 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.veq.not_vgt · cited by 0veq.not_vgtSemiring · cited by 13802SemiringValuativeRel · cited by 241ValuativeRelValuativeRel.vlt · cited by 49ValuativeRel.vltValuativeRel.veq · cited by 27ValuativeRel.veqValuativeRel.veq.vle · cited by 4veq.vleValuativeRel.vle.not_vlt · cited by 2vle.not_vltValuativeRel.not_vgt_of_veqCITED BYCITES

Cites6

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Cited by1

Results whose statement or proof uses this declaration.