Theorems · Theorem · commutative algebra
Valuation.restrict_le_one_iff
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
{x : R}, v.restrict x ≤ 1 ↔ v x ≤ 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- map_oneproof · cited by 861
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement · cited by 166
- Valuation.restrictstatement · cited by 112
- MonoidWithZeroHom.ValueGroup₀.embeddingproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- Valued.isClosed_integerproof · cited by 2
- Valued.isOpen_integerproof · cited by 2
- Valuation.isOpen_integerproof · cited by 2
- Valuation.isClosed_integerproof · cited by 2
- Padic.withValUniformEquiv_norm_le_one_iffproof · cited by 0
- Valuation.IsEquiv.valuedCompletion_le_one_iffproof · cited by 0