withTopWithBot' — Mathlib

English

Adjoins both top and bottom to the codomain, producing a bounded lattice homomorphism from WithTop(WithBot α) to β.

Русский

Добавляет и верхнюю границу, и нижнюю границу к кодомапу, образуя ограниченный гомоморфизм.

LaTeX

$$$ \\text{withTopWithBot}'(f) = \\langle f.withBot'.withTop', \\text{rfl}, \\text{rfl} \\rangle $$$

Lean4

/-- Adjoins a `⊤` and `⊥` to the codomain of a `LatticeHom`. -/
@[simps]
def withTopWithBot' [BoundedOrder β] (f : LatticeHom α β) : BoundedLatticeHom (WithTop <| WithBot α) β
    where
  toLatticeHom := f.withBot'.withTop'
  map_top' := rfl
  map_bot' := rfl

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