new set notations

Stream: general

[Patrick Massot]

I'm a bit disappointed that the new set notation doesn't seem to be defeq to set.image:

import data.set.basic

open set

example (f : ℕ → ℕ) (s : set ℕ) (h : 1 ∈ s) : f 1 ∈ f '' s :=
mem_image_of_mem f h

example (f : ℕ → ℕ) (s : set ℕ) (h : 1 ∈ s) : f 1 ∈ {(f x) | x ∈ s} :=
mem_image_of_mem f h -- doesn't work

Is this something that could be fixed? Or should we duplicate the whole set.image API?

[Johan Commelin]

Maybe it's time to redefine image?

[Mario Carneiro]

I think you should just live with the difference. The new notation also gives something different when you use more binders, i.e. {(f x y) | x y ∈ s} doesn't express anything that can be defined in terms of image or the 1D notation, so if we try to make a library around the notation version our work would never be done

[Mario Carneiro]

We could have a tactic (a simp proc - gasp!) to rewrite the new notation into an appropriate application of image

[Yury G. Kudryashov]

{(f x y) | x y ∈ s} is very similar to docs#set.image2

[Yury G. Kudryashov]

BTW, Lean doesn't use new notation for pretty-printing.