Theorems · Theorem · order theory
OrderIso.isCompl_iff
∀ {α : Type u_2} {β : Type u_3} [inst : Lattice α] [inst_1 : Lattice β] [inst_2 : BoundedOrder α]
[inst_3 : BoundedOrder β] (f : α ≃o β) {x y : α}, IsCompl x y ↔ IsCompl (f x) (f y)- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Latticestatement and proof · cited by 916
- OrderIsostatement and proof · cited by 874
- OrderIso.symmproof · cited by 475
- IsComplstatement and proof · cited by 351
- BoundedOrderstatement and proof · cited by 270
- OrderIso.symm_apply_applyproof · cited by 41
- OrderIso.isComplproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- OrderIso.complementedLatticeproof · cited by 4
- LieModule.isCompl_genWeightSpace_zero_posFittingCompproof · cited by 1
- Submodule.isCompl_comap_subtype_of_isCompl_of_leproof · cited by 0