Theorems · Definition · order theory
GaloisCoinsertion.liftLattice
{α : Type u} →
{β : Type v} →
{l : α → β} → {u : β → α} → [inst : PartialOrder β] → [inst_1 : Lattice α] → GaloisCoinsertion u l → Lattice βLift the suprema and infima along a Galois coinsertion
- Defined in
- Mathlib.Order.GaloisConnection.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrderLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Latticestatement and proof · cited by 916
- SemilatticeSupproof · cited by 785
- SemilatticeInfproof · cited by 634
- GaloisCoinsertionstatement and proof · cited by 35
- SemilatticeInf.infproof · cited by 3
- SemilatticeInf.inf_le_leftproof · cited by 2
- SemilatticeInf.inf_le_rightproof · cited by 2
- SemilatticeInf.le_infproof · cited by 1
- GaloisCoinsertion.liftSemilatticeInfproof · cited by 0
- GaloisCoinsertion.liftSemilatticeSupproof · cited by 0
Cited by1
Results whose statement or proof uses this declaration.
- GaloisCoinsertion.liftCompleteLatticeproof · cited by 0