Theorems · Theorem · commutative algebra
Valuation.map_sub_swap
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
(x y : R), v (x - y) = v (y - x)- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 23 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 · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- Valuation.toMonoidWithZeroHomproof · cited by 16
- MonoidHom.map_sub_swapproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Valued.isClosed_closedBallproof · cited by 4
- Valuation.isClosed_closedBallproof · cited by 4
- Padic.isUniformInducing_cast_withValproof · cited by 2
- Valuation.map_sub_of_right_eq_zeroproof · cited by 1
- Valuation.inversion_estimateproof · cited by 1
- AddValuation.map_sub_swapproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.exists_valuation_sub_lt_of_integerproof · cited by 0