Theorems · Theorem · order theory
GaloisConnection.monotone_u
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {l : α → β} {u : β → α},
GaloisConnection l u → Monotone u- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.le.transproof · cited by 3,151
- Monotonestatement · cited by 1,397
- GaloisConnectionstatement and proof · cited by 253
- GaloisConnection.l_u_leproof · cited by 36
- GaloisConnection.le_uproof · cited by 15
Cited by54
Results whose statement or proof uses this declaration.
- GaloisConnection.u_l_u_eq_uproof · cited by 17
- Filter.comap_monoproof · cited by 16
- GaloisInsertion.u_le_u_iffproof · cited by 10
- nhds_monoproof · cited by 6
- TopologicalSpace.generateFrom_antiproof · cited by 6
- CategoryTheory.Sieve.pullback_monotoneproof · cited by 6
- CategoryTheory.MorphismProperty.antitone_rlpproof · cited by 6
- Int.floor_monoproof · cited by 5
- GaloisConnection.isGLB_u_imageproof · cited by 4
- Submonoid.monotone_comapproof · cited by 4
- GaloisConnection.map_isCofinalproof · cited by 3
- ENat.card_le_card_of_injectiveproof · cited by 3