Theorems · Theorem · commutative algebra
Valuation.restrict_def
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
(x : R), v.restrict x = (MonoidWithZeroHom.ValueGroup₀.restrict₀ (MonoidWithZeroHom.ofClass v)) x- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 78 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 · 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
- MonoidWithZeroHomstatement · cited by 704
- 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.restrict₀statement · cited by 32
Cited by8
Results whose statement or proof uses this declaration.
- Valuation.exists_div_eq_of_unitproof · cited by 2
- Valued.continuous_extensionproof · cited by 2
- Valued.valuedCompletion_surjective_iffproof · cited by 2
- Valued.continuous_valuation_of_surjectiveproof · cited by 2
- LaurentSeries.inducing_coeproof · cited by 1
- Valued.closure_coe_completion_v_ltproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.uniformContinuous_algebraMap_liesOverproof · cited by 0
- WithVal.valueGroupOrderIso₀_symm_restrictproof · cited by 0