Theorems · Theorem · commutative algebra
Valuation.map_sub_of_left_eq_zero
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
{x y : R}, v x = 0 → v (x - y) = v y- 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
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- max_selfproof · cited by 43
- Valuation.map_subproof · cited by 3
- Valuation.map_sub_eq_of_lt_rightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.map_sub_of_right_eq_zeroproof · cited by 1
- Valuation.map_add_of_left_eq_zeroproof · cited by 1