Separating lattice homomorphism

Let [math]\displaystyle{ \mathbb{L} }[/math] and [math]\displaystyle{ \mathbb{L}' }[/math] be two lattices with 0 and 1. A homomorphism from [math]\displaystyle{ \mathbb{L} }[/math] to [math]\displaystyle{ \mathbb{L}' }[/math] is called 0,1-separating iff [math]\displaystyle{ f^{-1}\{f(0)\}=\{0\} }[/math] ([math]\displaystyle{ f }[/math] separates 0) and [math]\displaystyle{ f^{-1}\{f(1)\}=\{1\} }[/math] ([math]\displaystyle{ f }[/math] separates 1).