Theorems · Theorem · commutative algebra
Valuation.restrict_inj
∀ {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
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement · cited by 204
- MonoidWithZeroHom.ValueGroup₀statement · cited by 166
- Valuation.restrictstatement · cited by 112
- Valuation.embedding_restrictproof · cited by 9
- MonoidWithZeroHom.ValueGroup₀.embedding_injproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Valued.valuedCompletion_surjective_iffproof · cited by 2
- Valued.continuous_valuationproof · cited by 2
- Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integerproof · cited by 2
- LaurentSeries.tendsto_valuationproof · cited by 0