Theorems · Theorem · commutative algebra
Valuation.map_eq_of_sub_lt
∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : Ring R] [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] (v : Valuation R Γ₀)
{x y : R}, v (y - x) < v x → v y = v x- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- le_of_ltproof · cited by 1,175
- Valuationstatement and proof · cited by 823
- ne_of_gtproof · cited by 637
- sub_add_cancelproof · cited by 344
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- max_eq_rightproof · cited by 79
- Valuation.map_add_of_distinct_valproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- ModP.preVal_mkproof · cited by 5
- Valued.locally_constproof · cited by 3
- Valuation.inversion_estimateproof · cited by 1
- AddValuation.map_eq_of_lt_subproof · cited by 0
- LaurentSeries.tendsto_valuationproof · cited by 0
- IsValuativeTopology.continuous_valuationproof · cited by 0
- Valuation.locally_constproof · cited by 0