Theorems · Theorem · order theory
GaloisConnection.l_u_le
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {u : α → β} {l : β → α},
GaloisConnection l u → ∀ (a : α), l (u a) ≤ a- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- GaloisConnectionstatement and proof · cited by 253
- GaloisConnection.l_leproof · cited by 28
Cited by36
Results whose statement or proof uses this declaration.
- GaloisConnection.monotone_uproof · cited by 53
- GaloisInsertion.l_u_eqproof · cited by 37
- Int.floor_leproof · cited by 30
- GaloisConnection.l_u_l_eq_lproof · cited by 19
- GaloisConnection.u_l_u_eq_uproof · cited by 17
- Ideal.map_comap_leproof · cited by 14
- Filter.map_comap_leproof · cited by 10
- Cardinal.ord_card_leproof · cited by 6
- Submodule.map_comap_leproof · cited by 6
- GaloisConnection.isGreatest_uproof · cited by 3
- Subgroup.map_comap_leproof · cited by 3
- GaloisConnection.u_uniqueproof · cited by 3