English
Given a Galois coinsertion l ∘ u between α and β, one can lift the lattice structure from β to α, obtaining a lattice on α.
Русский
С данными полосой Галоикоассирования l и u между α и β можно перенести структуру решётки из β на α, получив структуру решётки на α.
LaTeX
$$$(Lattice\;β) \land (GaloisCoinsertion\; l\; u) \Rightarrow Lattice\;α$$$
Lean4
/-- Lift the suprema and infima along a Galois coinsertion -/
abbrev liftLattice [Lattice β] (gi : GaloisCoinsertion l u) : Lattice α :=
{ gi.liftSemilatticeSup, gi.liftSemilatticeInf with }
-- See note [reducible non-instances]