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Theorems · Theorem · commutative algebra

Valuation.isNontrivial_of_isEquiv

∀ {R : Type u_3} {Γ₀ : Type u_4} {Γ'₀ : Type u_5} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀]
  [inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] {v : Valuation R Γ₀} {v' : Valuation R Γ'₀},
  v.IsEquiv v' → v.IsNontrivial → v'.IsNontrivial
Defined in
Mathlib.RingTheory.Valuation.Basic
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext
Assumes
RingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Valuation.IsEquiv.isNontrivial_iff · cited by 1IsEquiv.isNontrivial_iffDFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingValuation · cited by 823ValuationLinearOrderedCommMonoidWithZero · cited by 139LinearOrderedCommMonoidWi…Valuation.IsEquiv · cited by 67Valuation.IsEquivValuation.IsNontrivial · cited by 27Valuation.IsNontrivialValuation.IsEquiv.eq_zero · cited by 11IsEquiv.eq_zeroValuation.IsEquiv.eq_one_iff_eq_one · cited by 5IsEquiv.eq_one_iff_eq_oneValuation.IsNontrivial.casesOn · cited by 3IsNontrivial.casesOnValuation.isNontrivial_of_isE…CITED BYCITES

Cites9

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Cited by1

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