Theorems · Theorem · order theory
max_zero_add_max_neg_zero_eq_abs_self
∀ {G : Type u_1} [inst : AddCommGroup G] [inst_1 : LinearOrder G] [IsOrderedAddMonoid G] (a : G),
max a 0 + max (-a) 0 = |a|- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- absstatement and proof · cited by 1,814
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- le_totalproof · cited by 294
- sup_of_le_leftproof · cited by 218
- sup_of_le_rightproof · cited by 143
- abs_eq_selfproof · cited by 59
- abs_eq_neg_selfproof · cited by 14
- Left.neg_nonpos_iffproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_negproof · cited by 0