Theorems · Theorem · order theory
negPart_add_posPart
∀ {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
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
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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
- neg_add_cancelproof · cited by 256
- le_sup_rightproof · cited by 242
- abs_nonnegproof · cited by 168
- PosPart.posPartstatement · cited by 113
- NegPart.negPartstatement and proof · cited by 107
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