Theorems · Theorem · order theory
abs_abs_sub_abs_le_abs_sub
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] (a b : G),
||a| - |b|| ≤ |a - b|- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, 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.
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- abs_sub_commproof · cited by 40
- abs_sub_le_iffproof · cited by 34
- abs_sub_abs_le_abs_subproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Rat.uniformContinuous_absproof · cited by 0
- Real.uniformContinuous_absproof · cited by 0