Theorems · Theorem · order theory
abs_le
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] {a b : G},
|a| ≤ b ↔ -b ≤ a ∧ a ≤ b- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 28 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 · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_leproof · cited by 27
- abs_le'proof · cited by 4
Cited by64
Results whose statement or proof uses this declaration.
- abs_sub_le_iffproof · cited by 34
- interior_closedBallproof · cited by 8
- InnerProductGeometry.angle_eq_pi_iffproof · cited by 8
- Polynomial.Chebyshev.abs_eval_T_real_le_oneproof · cited by 7
- le_of_abs_leproof · cited by 7
- Real.sin_le_oneproof · cited by 6
- Complex.re_le_normproof · cited by 5
- neg_le_of_abs_leproof · cited by 5
- InnerProductGeometry.angle_eq_zero_iffproof · cited by 5
- RCLike.re_le_normproof · cited by 5
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- Complex.sin_argproof · cited by 4