This PR adds a `sym =>` tactic that enters an interactive symbolic
simulation
mode built on `grind`. Unlike `grind =>`, it does not eagerly introduce
hypotheses or apply by-contradiction, giving users explicit control over
`intro`, `apply`, and `internalize` steps.
New tactics available in `sym =>` mode:
- `intro` / `intros`: introduce binders and internalize into the E-graph
by
default. Use `intro~` or `intro (internalize := false)` to skip
internalization.
- `apply t`: apply backward rules with caching for `repeat`.
- `internalize` / `internalize_all`: internalize hypotheses into the
E-graph.
- `by_contra`: apply proof by contradiction, negating the target.
Satellite solvers (`lia`, `ring`, `linarith`) automatically introduce
remaining
binders and apply by-contradiction in `sym =>` mode, matching their
behavior in
default tactic mode. All existing `grind =>` tactics (`finish`,
`instantiate`,
`cases`, etc.) also work in `sym =>` mode. The sym-specific tactics are
guarded
and rejected in regular `grind =>` mode.
```lean
example (x : Nat) : myP x → myQ x := by
sym [myP_myQ] =>
intro h
finish
example (x y z : Nat) : x > 1 → x + y + z > 0 := by
sym =>
lia
```
