Theorems · Theorem · order theory
posPart_sub_negPart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] (a : α), a⁺ - a⁻ = a- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeAddGroupAddLeftMono
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.
- AddGroupstatement and proof · cited by 4,410
- add_zeroproof · cited by 2,707
- sub_eq_add_negproof · cited by 1,023
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- add_neg_cancelproof · cited by 213
- sup_commproof · cited by 165
- PosPart.posPartstatement and proof · cited by 113
- NegPart.negPartstatement and proof · cited by 107
- add_neg_eq_iff_eq_addproof · cited by 12
- negPart_defproof · cited by 6
- add_supproof · cited by 6
Cited by9
Results whose statement or proof uses this declaration.
- CFC.posPart_sub_negPartproof · cited by 10
- abs_sub_eq_two_nsmul_negPartproof · cited by 1
- abs_add_eq_two_nsmul_posPartproof · cited by 1
- locallyFinsuppWithin.logCounting_divisorproof · cited by 1
- posPart_negPart_injectiveproof · cited by 1
- ValueDistribution.log_counting_zero_sub_logCounting_topproof · cited by 1
- le_iff_posPart_negPartproof · cited by 1
- posPart_inf_negPart_eq_zeroproof · cited by 0
- negPart_sub_posPartproof · cited by 0