Theorems · Theorem · order theory
OrderIso.le_symm_apply
∀ {α : Type u_2} {β : Type u_3} [inst : LE α] [inst_1 : LE β] (e : α ≃o β) {x : α} {y : β}, x ≤ e.symm y ↔ e x ≤ y- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, 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
- OrderIso.symmstatement · cited by 475
- RelIso.rel_symm_applyproof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- OrderIso.to_galoisConnectionproof · cited by 32
- le_negproof · cited by 16
- le_inv'proof · cited by 5
- Order.enum_le_of_forall_ltproof · cited by 3
- Subgroup.toAddSubgroup_closureproof · cited by 3
- OrderIso.upperBounds_imageproof · cited by 3
- upperClosure_imageproof · cited by 3
- OrderIso.apply_blimsupproof · cited by 2
- Submonoid.toAddSubmonoid_closureproof · cited by 0
- Subsemigroup.toAddSubsemigroup_closureproof · cited by 0
- AddSubsemigroup.toSubsemigroup'_closureproof · cited by 0