Theorems · Theorem · order theory
AbsoluteValue.abs_abv_sub_le_abv_sub
∀ {R : Type u_5} {S : Type u_6} [inst : Ring R] [inst_1 : CommRing S] [inst_2 : LinearOrder S] [IsStrictOrderedRing S]
(abv : AbsoluteValue R S) (a b : R), |abv a - abv b| ≤ abv (a - b)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- CommRingstatement and proof · cited by 17,173
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- IsStrictOrderedRingstatement and proof · cited by 2,490
- absstatement · cited by 1,814
- AbsoluteValuestatement and proof · cited by 363
- abs_sub_le_iffproof · cited by 34
- AbsoluteValue.map_subproof · cited by 6
- AbsoluteValue.le_subproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsAbsoluteValue.abs_abv_sub_le_abv_subproof · cited by 0