Theorems · Theorem · order theory
max_zero_sub_max_neg_zero_eq_self
∀ {α : Type u_1} [inst : AddGroup α] [inst_1 : LinearOrder α] [AddLeftMono α] (a : α), max a 0 - max (-a) 0 = a- Defined in
- Mathlib.Algebra.Order.Group.MinMax
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- zero_addproof · cited by 2,366
- sub_zeroproof · cited by 938
- AddLeftMonostatement and proof · cited by 687
- le_totalproof · cited by 294
- sub_neg_eq_addproof · cited by 264
- sup_of_le_leftproof · cited by 218
- sup_of_le_rightproof · cited by 143
- Left.neg_nonpos_iffproof · cited by 14
- Left.nonneg_neg_iffproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- max_neg_zeroproof · cited by 3
- MeasureTheory.integral_eq_integral_pos_part_sub_integral_neg_partproof · cited by 3
- max_zero_sub_eq_selfproof · cited by 2
- ProbabilityTheory.strong_law_ae_realproof · cited by 2
- CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_negproof · cited by 1
- BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_negproof · cited by 1