Theorems · Theorem · order theory
mabs_mul_eq_oneLePart_sq
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : CommGroup α] [MulLeftMono α] (a : α), |a|ₘ * a = a⁺ᵐ ^ 2- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeCommGroupMulLeftMono
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.
- CommGroupstatement and proof · cited by 990
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- sqproof · cited by 280
- mabsstatement and proof · cited by 148
- LeOnePart.leOnePartproof · cited by 41
- OneLePart.oneLePartstatement and proof · cited by 40
- oneLePart_div_leOnePartproof · cited by 6
- oneLePart_mul_leOnePartproof · cited by 2
- mul_mul_div_cancelproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- mul_mabs_eq_oneLePart_sqproof · cited by 0