Theorems · Definition · order theory
OrderIso.inv
(α : Type u) → [inst : Group α] → [inst_1 : LE α] → [MulLeftMono α] → [MulRightMono α] → α ≃o αᵒᵈ
x ↦ x⁻¹ as an order-reversing equivalence.
- Defined in
- Mathlib.Algebra.Order.Group.OrderIso
- Cited by
- 27 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.invproof · cited by 23
- inv_le_inv_iffproof · cited by 11
Cited by27
Results whose statement or proof uses this declaration.
- le_inv'proof · cited by 5
- inv_le'proof · cited by 5
- inv_infproof · cited by 3
- inv_supproof · cited by 3
- csInf_invproof · cited by 1
- bddAbove_invproof · cited by 1
- isLUB_inv'proof · cited by 1
- Filter.map_inv_atBotproof · cited by 1
- Filter.map_inv_atTopproof · cited by 1
- Filter.tendsto_inv_atTop_atBotproof · cited by 1
- isGLB_inv'proof · cited by 1
- sInf_invproof · cited by 1