Theorems · Theorem · commutative algebra
Valuation.map_sub_eq_of_lt_left
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
{x y : R}, v y < v x → v (x - y) = v x- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- sub_eq_add_negproof · cited by 1,023
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.map_negproof · cited by 11
- Valuation.map_add_eq_of_lt_leftproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Valued.isClosed_closedBallproof · cited by 4
- Valuation.isClosed_closedBallproof · cited by 4