prodEquiv — Mathlib

English

The product of Sublattices L.prod M is order-isomorphic to the ordinary product lattice L × M.

Русский

Произведение подпределов L.prod M изоморфно по порядку обычному произведению латиц L × M.

LaTeX

$$L.prod M \\cong_o L \\times M$$

Lean4

/-- The product of sublattices is isomorphic to their product as lattices. -/
@[simps! toEquiv apply symm_apply]
def prodEquiv (L : Sublattice α) (M : Sublattice β) : L.prod M ≃o L × M
    where
  toEquiv := Equiv.Set.prod _ _
  map_rel_iff' := Iff.rfl

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