Theorems · Theorem · commutative algebra
Valuation.map_neg
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
(x : R), v (-x) = v x- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 11 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_negproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- Valuation.map_subproof · cited by 3
- Valuation.map_sub_eq_of_lt_leftproof · cited by 2
- Valuation.isEquiv_iff_val_eq_oneproof · cited by 2
- Valuation.map_sub_eq_of_lt_rightproof · cited by 1
- Valuation.map_sub_leproof · cited by 1
- Valuation.Integers.isIntegral_iff_v_le_oneproof · cited by 1
- Valuation.map_add_of_left_eq_zeroproof · cited by 1
- AddValuation.map_negproof · cited by 1
- Valuation.map_one_sub_of_ltproof · cited by 0
- Valuation.coeff_zero_minpolyproof · cited by 0
- Valuation.map_sub_ltproof · cited by 0