Theorems · Theorem · order theory
GaloisInsertion.l_surjective
∀ {α : Type u} {β : Type v} {l : α → β} {u : β → α} [inst : Preorder α] [inst_1 : PartialOrder β]
(gi : GaloisInsertion l u), Function.Surjective l- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- 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
- GaloisInsertionstatement and proof · cited by 35
- Function.LeftInverse.surjectiveproof · cited by 22
- GaloisInsertion.leftInverse_l_uproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- AddSubsemigroup.map_surjective_of_surjectiveproof · cited by 0
- Submonoid.map_surjective_of_surjectiveproof · cited by 0
- Ideal.map_surjective_of_surjectiveproof · cited by 0
- DiffeologicalSpace.generateFrom_surjectiveproof · cited by 0
- AddSubmonoid.map_surjective_of_surjectiveproof · cited by 0
- Subsemigroup.map_surjective_of_surjectiveproof · cited by 0
- FirstOrder.Language.Substructure.map_surjective_of_surjectiveproof · cited by 0
- Ordinal.pred_surjectiveproof · cited by 0
- Submodule.map_surjective_of_surjectiveproof · cited by 0