Theorems · Theorem · commutative algebra
Valuation.restrict_lt_iff_lt_embedding
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
{x : R} {g : (MonoidWithZeroHom.ofClass v).ValueGroup₀},
v.restrict x < g ↔ v x < MonoidWithZeroHom.ValueGroup₀.embedding g- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 10 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.
Cites15
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
- MonoidWithZeroHomstatement · cited by 704
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement and proof · cited by 166
- Valuation.restrictstatement · cited by 112
- StrictMono.lt_iff_ltproof · cited by 86
Cited by10
Results whose statement or proof uses this declaration.
- Valuation.restrict_lt_iffproof · cited by 8
- Valuation.subgroups_basisproof · cited by 5
- Padic.isUniformInducing_cast_withValproof · cited by 2
- LaurentSeries.uniformContinuous_coeffproof · cited by 2
- Valued.tendsto_zero_pow_of_v_lt_oneproof · cited by 1
- Valuation.discreteTopology_of_forall_map_eq_oneproof · cited by 1
- LaurentSeries.inducing_coeproof · cited by 1
- Valued.discreteTopology_of_forall_map_eq_oneproof · cited by 1
- LaurentSeries.Cauchy.eventually_mem_nhdsproof · cited by 0
- Valuation.restrict_lt_one_iffproof · cited by 0