Theorems · Theorem · order theory
posPart_inf_negPart_eq_zero
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] [AddRightMono α] (a : α), a⁺ ⊓ a⁻ = 0- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
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Cites14
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
- zero_addproof · cited by 2,366
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- AddRightMonostatement and proof · cited by 367
- add_neg_cancelproof · cited by 213
- PosPart.posPartstatement and proof · cited by 113
- NegPart.negPartstatement and proof · cited by 107
- add_left_injproof · cited by 36
- posPart_sub_negPartproof · cited by 9
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