Theorems · Theorem · order theory
GaloisConnection.map_isCofinal
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : β → α} {g : α → β},
GaloisConnection f g → ∀ {s : Set α}, IsCofinal s → IsCofinal (g '' s)- Defined in
- Mathlib.Order.Cofinal
- Cited by
- 3 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.
Cites8
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 · cited by 5,609
- GaloisConnectionstatement and proof · cited by 253
- IsCofinalstatement and proof · cited by 84
- GaloisConnection.monotone_uproof · cited by 53
- IsCofinal.imageproof · cited by 4
- GaloisConnection.isCofinal_rangeproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- GaloisConnection.cof_le_liftproof · cited by 2
- OrderIso.map_isCofinalproof · cited by 2
- GaloisConnection.map_cofinalproof · cited by 0