Quick Mycosynth Lattice Question

[riggy]

I know how Mycosynth Lattice works with regards to Workshop, but at what point does a "colorless spell on the stack" become an "artifact enchantment"? Will it trigger Come into Play abilities that trigger on artifacts?

For example, my opponent casts an enchantment with Lattice and a Arcbound Crusher in play. Will the crusher get a counter for the enchantment? And could you please point to the rule that will clarify this sort of question?

Oracle Text:
Mycosynth Lattice

Artifact
All permanents are artifacts in addition to their other types.
All cards that aren't in play, spells, and permanents are colorless.
Players may spend mana as though it were mana of any color.

Thanks in advance.

[Jebus]

It will come into play as an artifact and trigger the Crusher.

Relevant rule:

418.2. Continuous effects that modify characteristics of permanents do so simultaneously with the permanent coming into play. They don’t wait until the permanent is in play and then change it. Because such effects apply as the permanent comes into play, apply them before determining whether the permanent will cause an ability to trigger when it comes into play.