Theorems · Theorem · order theory
neg_le_of_abs_le
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] {a b : G}, |a| ≤ b → -b ≤ a- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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_leproof · cited by 64
Cited by5
Results whose statement or proof uses this declaration.
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
- Polynomial.Chebyshev.abs_eval_T_real_eq_one_iffproof · cited by 3
- Int.nneg_mul_add_sq_of_abs_le_oneproof · cited by 1
- neg_one_le_real_inner_of_norm_eq_oneproof · cited by 1
- balancedHull_subset_convexHull_union_negproof · cited by 1