Theorems · Theorem · order theory
OrderIso.apply_eq_iff_eq
∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) {x y : α}, e x = e y ↔ x = y- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- OrderIsostatement and proof · cited by 874
- RelIso.toEquivproof · cited by 113
- Equiv.apply_eq_iff_eqproof · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- IsGalois.fixedField_eq_iff_fixingSubgroup_eqproof · cited by 0
- IsSuccArchimedean.of_orderIsoproof · cited by 0
- IsPredArchimedean.of_orderIsoproof · cited by 0