Remark: the main motivation for piext was Lean 0.1 simplifier.
We are using a different approach in Lean 0.2.
The axiom is not needed anymore.
It is also not used in any part of the standard library
I made some major changes in the library. I wanted to wait with pushing
until I had finished the formalization of the slice functor, but for
some reason that is very hard to formalize, requiring a lot of casts and
manipulation of casts. So I've not finished that yet.
Changes:
- in multiple files make more use of variables
- move dependent congr_arg theorems to logic.cast and proof them using heq (which doesn't involve nested inductions and fewer casts).
- prove some more theorems involving heq, e.g. hcongr_arg3 (which do not
require piext)
- in theorems where casts are used in the statement use eq.rec_on
instead of eq.drec_on
- in category split basic into basic, functor and natural_transformation
- change the definition of functor to use fully bundled
categories. @avigad: this means that the file semisimplicial.lean will
also need changes (but I'm quite sure nothing major). You want to
define the fully bundled category Delta, and use only fully bundled
categories (type and ᵒᵖ are notations for the fully bundled
Type_category and Opposite if you open namespace category.ops). If you
want I can make the changes.
- lots of minor changes
