Theorems · Theorem · order theory
max_sub_min_eq_abs
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] [AddRightMono α] (a b : α),
max a b - min a b = |b - a|- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- AddGroupstatement and proof · cited by 4,410
- absstatement and proof · cited by 1,814
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- abs_sub_commproof · cited by 40
- max_sub_min_eq_abs'proof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Set.abs_sub_le_of_uIcc_subset_uIccproof · cited by 3
- Real.volume_uIocproof · cited by 2
- Real.volume_intervalproof · cited by 1
- intervalIntegral.norm_integral_le_of_norm_le_const_aeproof · cited by 1
- unitInterval.volume_uIccproof · cited by 0
- unitInterval.volume_uIocproof · cited by 0
- unitInterval.volume_uIooproof · cited by 0
- Real.volume_uIooproof · cited by 0
- Int.card_uIccproof · cited by 0
- dist_inf_sup_piproof · cited by 0