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Theorems · Theorem · commutative algebra

ValuativeRel.subsingleton_units_valueGroupWithZero_of_trivialRel

∀ (R Γ : Type) [inst : Ring R] [inst_1 : DecidableEq R] [inst_2 : IsDomain R]
  [inst_3 : LinearOrderedCommGroupWithZero Γ] [inst_4 : ValuativeRel R] [Valuation.Compatible 1],
  Subsingleton (ValuativeRel.ValueGroupWithZero R)ˣ
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Trivial
Cited by
2 results in Mathlib
Foundations
Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingDecidableEqIsDomainLinearOrderedCommGroupWithZeroValuativeRelValuation.Compatible
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Around this declaration

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

ValuativeRel.not_isNontrivial_of_trivialRel · cited by 0ValuativeRel.not_isNontri…ValuativeRel.isDiscrete_trivialRel · cited by 0ValuativeRel.isDiscrete_t…DFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463Ringmul_one · cited by 3885mul_oneUnits · cited by 2804UnitsIsDomain · cited by 2196IsDomainUnits.val · cited by 1966Units.valmap_mul · cited by 1137map_mulValuation · cited by 823ValuationLinearOrderedCommGroupWithZero · cited by 528LinearOrderedCommGroupWit…ValuativeRel · cited by 241ValuativeRelValuativeRel.ValueGroupWithZero · cited by 86ValuativeRel.ValueGroupWi…Valuation.Compatible · cited by 71Valuation.CompatibleValuation.IsEquiv · cited by 67Valuation.IsEquivValuativeRel.posSubmonoid · cited by 45ValuativeRel.posSubmonoidValuativeRel.valuation · cited by 42ValuativeRel.valuationValuativeRel.subsingleton_uni…CITED BYCITES

Cites21

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Cited by2

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