Theorems · Definition · order theory
OrderIso.divLeft
{α : Type u} → [inst : Group α] → [inst_1 : LE α] → [MulLeftMono α] → [MulRightMono α] → α → α ≃o αᵒᵈx ↦ a / x as an order-reversing equivalence.
- Defined in
- Mathlib.Algebra.Order.Group.OrderIso
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 16 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.
- Equivproof · cited by 8,337
- Groupstatement and proof · cited by 6,238
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- OrderDual.toDualproof · cited by 481
- MulLeftMonostatement and proof · cited by 410
- Equiv.transproof · cited by 337
- MulRightMonostatement and proof · cited by 263
- Equiv.divLeftproof · cited by 7
- div_le_div_iff_leftproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- div_infproof · cited by 1
- div_supproof · cited by 1
- OrderIso.divLeft_applystatement and proof · cited by 0
- OrderIso.divLeft_symm_applystatement and proof · cited by 0