Theorems · Theorem · order theory
abs_min_sub_min_le_max
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α] (a b c d : α),
|min a b - min c d| ≤ max |a - c| |b - d|- Defined in
- Mathlib.Algebra.Order.Group.MinMax
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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_sub_commproof · cited by 40
- neg_sub_negproof · cited by 13
- abs_max_sub_max_le_maxproof · cited by 5
- max_neg_negproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- lipschitzWith_minproof · cited by 2
- CauSeq.inf_equiv_infproof · cited by 1
- Set.abs_projIcc_sub_projIccproof · cited by 1
- CauSeq.rat_inf_continuous_lemmaproof · cited by 0