That "analytic" style you suggest is really interesting, too. I'm not sure I have a dog in the ultimate race and I'd love to see both analytic and synthetic styles flourish, but from a mere terminology point of view I'd distinguish between the two languages in means of describing them as "pure" or not.

I also really worry that external proofs will ultimately be neglected in practice. I suppose this is again a "UX of Types" thing, but I'm something of a believer that anything that you do not literally demand of the programmer will eventually be sacrificed.