Theorems · Definition · order theory
upperSetIsoLowerSet
{α : Type u_1} → [inst : LE α] → UpperSet α ≃o LowerSet αUpper sets are order-isomorphic to lower sets under complementation.
- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LE
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.
- OrderIsostatement · cited by 874
- UpperSetstatement and proof · cited by 245
- LowerSetstatement · cited by 230
- LowerSet.complproof · cited by 17
- UpperSet.complproof · cited by 17
- LowerSet.compl_complproof · cited by 0
- UpperSet.compl_complproof · cited by 0
- UpperSet.compl_le_complproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- upperSetIsoLowerSet_applystatement and proof · cited by 0
- upperSetIsoLowerSet_symm_applystatement and proof · cited by 0