Theorems · Theorem · order theory
le_of_abs_le
∀ {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
- 7 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 by7
Results whose statement or proof uses this declaration.
- Real.sin_ltproof · cited by 4
- ArchimedeanClass.exists_nat_ge_of_mk_nonnegproof · cited by 3
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
- Int.nneg_mul_add_sq_of_abs_le_oneproof · cited by 1
- NNReal.le_add_nndistproof · cited by 1
- ODE.FunSpace.dist_iterate_next_apply_leproof · cited by 1
- balancedHull_subset_convexHull_union_negproof · cited by 1