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Theorems · Theorem · commutative algebra

Valuation.map_one_add_of_lt

∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
  {x : R}, v x < 1 → v (1 + x) = 1
Defined in
Mathlib.RingTheory.Valuation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingLinearOrderedCommMonoidWithZero
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Around this declaration

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

ValuationSubring.unitGroup_le_unitGroup · cited by 0ValuationSubring.unitGrou…ValuationSubring.principal_units_le_units · cited by 0ValuationSubring.principa…DFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingValuation · cited by 823ValuationLinearOrderedCommMonoidWithZero · cited by 139LinearOrderedCommMonoidWi…Valuation.map_one · cited by 17Valuation.map_oneValuation.map_add_eq_of_lt_left · cited by 6Valuation.map_add_eq_of_l…Valuation.map_one_add_of_ltCITED BYCITES

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Cited by2

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