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Theorems · Theorem · commutative algebra

ValuativeRel.div_vle_one_iff

∀ {K : Type u_2} [inst : DivisionRing K] [inst_1 : ValuativeRel K] {a b : K}, b ≠ 0 → (a / b ≤ᵥ 1 ↔ a ≤ᵥ b)
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Basic
Cited by
1 results in Mathlib
Foundations
Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
DivisionRingValuativeRel
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Around this declaration

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

ValuativeRel.inv_vle_one · cited by 1ValuativeRel.inv_vle_oneone_mul · cited by 2841one_mulDivisionRing · cited by 1062DivisionRingValuativeRel · cited by 241ValuativeRelValuativeRel.vle · cited by 84ValuativeRel.vleValuativeRel.div_vle_iff · cited by 1ValuativeRel.div_vle_iffValuativeRel.div_vle_one_iffCITED BYCITES

Cites5

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Cited by1

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