8353964e55
This PR wires the `PowIdentity` typeclass (from https://github.com/leanprover/lean4/pull/13086) into the `grind` ring solver's Groebner basis engine. When a ring has a `PowIdentity α p` instance, the solver pushes `x ^ p = x` as a new fact for each variable `x`, which becomes `x^p - x = 0` in the Groebner basis. Since `p` is an `outParam`, instance discovery is decoupled from `IsCharP` — the solver synthesizes `PowIdentity α ?p` with a fresh metavar and lets instance search find both the instance and the exponent. This correctly handles non-prime finite fields: for `F_4` (char 2, 4 elements), Mathlib would provide `PowIdentity F_4 4` and the solver would discover `p = 4`, not `p = 2`. Note: the original motivating example `(x + y)^2 = x^128 + y^2` from https://github.com/leanprover/lean4/issues/12842 does not yet work because the `ToInt` module lifts `Fin 2` expressions to integers and expands `x^128` via the binomial theorem before the ring solver can reduce it. Addressing that is a separate deeper change. 🤖 Prepared with Claude Code --------- Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
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126 B
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2 lines
126 B
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grind_ring_1.lean:59:0-59:7: warning: declaration uses `sorry`
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grind_ring_1.lean:72:0-72:7: warning: declaration uses `sorry`
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