Theorems · Definition · commutative algebra
AddValuation.toPreorder
{R : Type u_3} →
{Γ₀ : Type u_4} → [inst : Ring R] → [inst_1 : LinearOrderedAddCommMonoidWithTop Γ₀] → AddValuation R Γ₀ → Preorder RA valuation gives a preorder on the underlying ring.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Preorderstatement · cited by 7,952
- Ringstatement and proof · cited by 7,463
- AddValuationstatement and proof · cited by 96
- LinearOrderedAddCommMonoidWithTopstatement and proof · cited by 68
- Preorder.liftproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.