Theorems · Theorem · order theory
oneLePart_div_leOnePart
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] (a : α), a⁺ᵐ / a⁻ᵐ = a- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeGroupMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Latticestatement and proof · cited by 916
- div_eq_mul_invproof · cited by 715
- MulLeftMonostatement and proof · cited by 410
- sup_commproof · cited by 165
- mul_inv_cancelproof · cited by 128
- LeOnePart.leOnePartstatement and proof · cited by 41
- OneLePart.oneLePartstatement and proof · cited by 40
- mul_inv_eq_iff_eq_mulproof · cited by 13
- mul_supproof · cited by 6
- leOnePart_defproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- mabs_mul_eq_oneLePart_sqproof · cited by 1
- oneLePart_leOnePart_injectiveproof · cited by 1
- mabs_div_eq_leOnePart_sqproof · cited by 1
- oneLePart_inf_leOnePart_eq_oneproof · cited by 0
- leOnePart_div_oneLePartproof · cited by 0
- le_iff_oneLePart_leOnePartproof · cited by 0