Theorems · Theorem · order theory
GaloisCoinsertion.u_surjective
∀ {α : Type u} {β : Type v} {u : α → β} {l : β → α} [inst : Preorder α] [inst_1 : PartialOrder β]
(gi : GaloisCoinsertion l u), Function.Surjective u- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderPartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- PartialOrderstatement and proof · cited by 6,410
- GaloisCoinsertionstatement and proof · cited by 35
- Function.LeftInverse.surjectiveproof · cited by 22
- GaloisCoinsertion.leftInverse_u_lproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- Submodule.comap_surjective_of_injectiveproof · cited by 1
- Submonoid.comap_surjective_of_injectiveproof · cited by 0
- AddSubmonoid.comap_surjective_of_injectiveproof · cited by 0
- Subsemigroup.comap_surjective_of_injectiveproof · cited by 0
- Submonoid.units_surjectiveproof · cited by 0
- FirstOrder.Language.Substructure.comap_surjective_of_injectiveproof · cited by 0
- AddSubsemigroup.comap_surjective_of_injectiveproof · cited by 0
- AddSubmonoid.addUnits_surjectiveproof · cited by 0
- Filter.ker_surjectiveproof · cited by 0
- TopologicalSpace.generateFrom_surjectiveproof · cited by 0