Theorems · Theorem · order theory
GaloisConnection.le_iff_le
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
GaloisConnection l u → ∀ {a : α} {b : β}, l a ≤ b ↔ a ≤ u b- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- GaloisConnectionstatement and proof · cited by 253
Cited by17
Results whose statement or proof uses this declaration.
- Cardinal.ord_leproof · cited by 10
- Ordinal.mul_le_iff_le_divproof · cited by 10
- isLUB_image2_of_isLUB_isLUBproof · cited by 7
- GaloisConnection.u_eq_topproof · cited by 4
- CategoryTheory.Sieve.functorPushforward_le_iff_le_functorPullbackproof · cited by 3
- Submodule.le_dualAnnihilator_iff_le_dualCoannihilatorproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.le_ofIdeals_iffproof · cited by 2
- Submonoid.prod_eq_bot_iffproof · cited by 1
- Int.zpow_le_iff_le_logproof · cited by 1
- AlgebraicGeometry.Scheme.Cover.toPresieveOver_le_arrows_iffproof · cited by 1
- AddSubmonoid.prod_eq_bot_iffproof · cited by 1
- Int.le_zpow_iff_clog_leproof · cited by 1