Theorems · Theorem · order theory
abs_sub_le
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] (a b c : G),
|a - c| ≤ |a - b| + |b - c|- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- sub_add_sub_cancelproof · cited by 56
- abs_add_leproof · cited by 17
Cited by6
Results whose statement or proof uses this declaration.
- Real.log_two_near_10proof · cited by 2
- Real.log_five_near_10proof · cited by 2
- Real.exp_approx_succproof · cited by 2
- IsCauSeq.of_abv_leproof · cited by 2
- Real.log_three_near_10proof · cited by 2
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2