Previously the `ac_rfl` tactic was only really usable when depending on
mathlib. With these instances, `ac_rfl` can deal with the various
operations defined in Lean.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This removes simp attributes from `Nat.succ.injEq` and
`Nat.succ_sub_succ_eq_sub` to replace them with simprocs. This is
because any reductions involving `Nat.succ` has a high risk of leading
proof performance problems when dealing with even moderately large
numbers.
Here are a couple examples that will both report a maximum recursion
depth error currently. These examples are fixed by this PR.
```
example : (123456: Nat) = 12345667 := by
simp
example (x : Nat) (p : x = 0) : 1000 - (x + 1000) = 0 := by
simp
```
This adds a number of lemmas for simplification of `Bool` and `Prop`
terms. It pulls lemmas from Mathlib and adds additional lemmas where
confluence or consistency suggested they are needed.
It has been tested against Mathlib using some automated test
infrastructure.
That testing module is not yet included in this PR, but will be included
as part of this.
Note. There are currently some comments saying the origin of the simp
rule. These will be removed prior to merging, but are added to clarify
where the rule came from during review.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
First (baby)-step to a `concat`-based `bitblast`: a characterization of
`concat` in terms of `getLsb`.
The proof might benefit slightly from a `toNat_concat` lemma, but I
wasn't sure what the normal form there should be, so I avoided it.
---------
Co-authored-by: Scott Morrison <scott@tqft.net>
