```
example (a : Nat) :
(((a + (2 ^ 64 - 1)) % 2 ^ 64 + 1) * 8 - 1 - (a + (2 ^ 64 - 1)) % 2 ^ 64 * 8 + 1) = 8 := by
omega
```
used to time out, and now is fast.
(We will probably make separate changes later so the defeq checks would
be fast in any case here.)
The current `ToExpr Int` instance produces `@Int.ofNat (@OfNat.ofNat Nat
i ...)` for nonnegative `i` and `@Int.negSucc (@OfNat.ofNat Nat (-i+1)
...)` for negative `i`.
However it should be producing `@OfNat.ofNat Int i ...` for nonnegative
`i`, and `@Neg.neg ... (@OfNat.ofNat Int (-i) ...)` for negative `i`.
This is very helpful when dealing with bitvectors, where a case analysis
on the bitwidth leaves one with hypotheses of the form `x<2^(Nat.succ
w)`.
Design decisions I am unsure about:
- Is creating a helper `succ?` the correct way to match on the exponent
`e+1`?
- I'm not certain why the prior call to `Int.ofNat_pow` also checked
that the exponent was a ground natural. I removed this, since we now
explicitly handle cases where the exponent is a term of the form `e+1`.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
Co-authored-by: Joe Hendrix <joe@lean-fro.org>
Co-authored-by: Alex Keizer <alex@keizer.dev>
