English
There exists a Galois insertion between ConvexCone R M and SetLike.coe, with hull R as the left adjoint to the coercion.
Русский
Существует Галуа-инсерция между ConvexCone R M и SetLike.coe, где hull R является левым дополнением к левому отображению.
LaTeX
$$Galois insertion between hull_R and coercion: hull_R s ≤ C ⇔ s ⊆ C for all s ⊆ M and C ∈ ConvexCone R M.$$
Lean4
/-- Galois insertion between `ConvexCone` and `SetLike.coe`. -/
protected def gi : GaloisInsertion (hull R : Set M → ConvexCone R M) (↑)
where
gc := gc_hull_coe
le_l_u _ := subset_hull
choice s hs := (hull R s).copy s <| subset_hull.antisymm hs
choice_eq _ _ := copy_eq _ _ _
