Theorems · Theorem · order theory
GaloisCoinsertion.leftInverse_u_l
∀ {α : Type u} {β : Type v} {u : α → β} {l : β → α} [inst : Preorder α] [inst_1 : PartialOrder β]
(gi : GaloisCoinsertion l u), Function.LeftInverse u l- Defined in
- Mathlib.Order.GaloisConnection.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderPartialOrder
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
- PartialOrderstatement and proof · cited by 6,410
- GaloisCoinsertionstatement and proof · cited by 35
- GaloisCoinsertion.u_l_eqproof · cited by 18
Cited by8
Results whose statement or proof uses this declaration.
- GaloisCoinsertion.l_injectiveproof · cited by 10
- GaloisCoinsertion.u_surjectiveproof · cited by 10
- AddSubgroup.ofAddUnits_right_inverseproof · cited by 0
- Submonoid.units_left_inverseproof · cited by 0
- GaloisCoinsertion.u_l_leftInverseproof · cited by 0
- Subgroup.ofUnits_right_inverseproof · cited by 0
- AddSubmonoid.addUnits_left_inverseproof · cited by 0
- TopologicalSpace.leftInverse_generateFromproof · cited by 0