Theorems · Theorem · commutative algebra
Valuation.coe_ltAddSubgroup
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
(γ : Γ₀ˣ), ↑(v.ltAddSubgroup γ) = {x | v x < ↑γ}- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Set.ofPredstatement · cited by 6,101
- AddSubgroupstatement · cited by 3,232
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.ltAddSubgroupstatement and proof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Valuation.subgroups_basisproof · cited by 5
- Valuation.toUniformSpace_eqproof · cited by 2
- Valued.toUniformSpace_eqproof · cited by 1