Theorems · Theorem · order theory
abs_sub_eq_two_nsmul_negPart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddCommGroup α] [AddLeftMono α] (a : α), |a| - a = 2 • a⁻- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- absstatement and proof · cited by 1,814
- Latticestatement and proof · cited by 916
- AddLeftMonostatement and proof · cited by 687
- PosPart.posPartproof · cited by 113
- NegPart.negPartstatement and proof · cited by 107
- two_nsmulproof · cited by 67
- add_sub_sub_cancelproof · cited by 14
- posPart_sub_negPartproof · cited by 9
- posPart_add_negPartproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- sub_abs_eq_neg_two_nsmul_negPartproof · cited by 0