Theorems · Theorem · order theory
oneLePart_mul_leOnePart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] [MulRightMono α] (a : α), a⁺ᵐ * a⁻ᵐ = |a|ₘ- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 2 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.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- le_sup_rightproof · cited by 242
- mabsstatement and proof · cited by 148
- mul_inv_cancelproof · cited by 128
- sup_eq_leftproof · cited by 71
- sup_eq_rightproof · cited by 53
- LeOnePart.leOnePartstatement and proof · cited by 41
Cited by2
Results whose statement or proof uses this declaration.
- mabs_mul_eq_oneLePart_sqproof · cited by 1
- mabs_div_eq_leOnePart_sqproof · cited by 1