instDistribLatticeCoe — Mathlib

English

The canonical lattice hom from a sublattice L to α is the inclusion map.

Русский

Каноническая латица-гомоморфизм от подрешетки L к α есть инклюзия.

LaTeX

$$$ \\text{def } \\text{subtype}(L) : LatticeHom L α $$$

Lean4

/-- A sublattice of a distributive lattice inherits a distributive lattice structure. -/
instance instDistribLatticeCoe {α : Type*} [DistribLattice α] (L : Sublattice α) : DistribLattice L :=
  Subtype.coe_injective.distribLattice _ (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)

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