Theorems · Theorem · commutative algebra
Valuation.restrict_lt_iff
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
{x y : R}, v.restrict x < v.restrict y ↔ v x < v y- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 8 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.
Cites12
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
- 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
- Valuation.restrict_lt_iff_lt_embeddingproof · cited by 10
- Valuation.embedding_restrictproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- Valued.locally_constproof · cited by 3
- Padic.isUniformInducing_cast_withValproof · cited by 2
- Valuation.IsEquiv.uniformContinuous_equivproof · cited by 2
- Valued.toNormedField.norm_lt_one_iffproof · cited by 1
- Valuation.IsEquiv.uniformContinuous_equiv_symmproof · cited by 1
- Valuation.locally_constproof · cited by 0
- Valued.toNormedField.norm_lt_iffproof · cited by 0
- Valued.toNormedField.one_lt_norm_iffproof · cited by 0