Theorems · Theorem · order theory
abs_le_max_abs_abs
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] {a b c : G},
a ≤ b → b ≤ c → |b| ≤ max |a| |c|- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- LE.le.transproof · cited by 3,151
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_abs_selfproof · cited by 113
- neg_le_neg_iffproof · cited by 57
- neg_le_absproof · cited by 18
- le_sup_iffproof · cited by 7
- abs_le'proof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.integrable_of_le_of_leproof · cited by 6
- ArchimedeanClass.min_le_mk_of_le_of_leproof · cited by 1
- ProbabilityTheory.variance_le_sub_mul_subproof · cited by 1
- MeasureTheory.memLp_of_boundedproof · cited by 1
- MeasureTheory.HasFiniteIntegral.of_mem_Iccproof · cited by 1