Theorems · Theorem · order theory
posPart_add_negPart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] [AddRightMono α] (a : α), a⁺ + a⁻ = |a|- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- zero_addproof · cited by 2,366
- absstatement and proof · cited by 1,814
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- le_sup_rightproof · cited by 242
- add_neg_cancelproof · cited by 213
- abs_nonnegproof · cited by 168
- PosPart.posPartstatement · cited by 113
- NegPart.negPartstatement and proof · cited by 107
Cited by3
Results whose statement or proof uses this declaration.
- CFC.posPart_add_negPartproof · cited by 2
- abs_add_eq_two_nsmul_posPartproof · cited by 1
- abs_sub_eq_two_nsmul_negPartproof · cited by 1