Theorems · Theorem · order theory
GaloisConnection.bddAbove_l_image
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
GaloisConnection l u → ∀ {s : Set α}, BddAbove (l '' s) ↔ BddAbove s- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.imagestatement and proof · cited by 5,609
- BddAbovestatement and proof · cited by 620
- upperBoundsproof · cited by 263
- GaloisConnectionstatement and proof · cited by 253
- GaloisConnection.monotone_lproof · cited by 76
- Monotone.map_bddAboveproof · cited by 9
- GaloisConnection.upperBounds_l_imageproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- OrderIso.bddAbove_imageproof · cited by 3
- Cardinal.bddAbove_ord_image_iffproof · cited by 1