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fix: relate casts from Nat and Int in grind rings - #16204
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This PR fixes `grind` failing on goals that mix a cast from `Nat` and a cast from `Int` into the same ring, such as `(m : Int) (k : Nat) (h : m = k) : (m : R) = (k : R)`. With the new normalizer (`backward.grind.normalizer false`) this also affected goals written as `(m : R) = ((k : Int) : R)`, because the normalizer rewrites `((k : Int) : R)` to `(k : R)`. A ring has two casts, `NatCast.natCast` and `IntCast.intCast`, and congruence only relates applications of the same function, so `↑m` and `↑k` stayed unrelated even when `m = ↑k`. The ring solver now asserts `((a : Int) : α) = ↑a` for each cast `↑a` of a non-numeral from `Nat`, but only once the ring contains a cast of a non-numeral from `Int`. The equation bypasses the normalizer, which would rewrite it to `↑a = ↑a`. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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This PR fixes
grindfailing on goals that mix a cast fromNatand a cast fromIntinto the same ring, such as(m : Int) (k : Nat) (h : m = k) : (m : R) = (k : R). With the new normalizer (backward.grind.normalizer false) this also affected goals written as(m : R) = ((k : Int) : R), because the normalizer rewrites((k : Int) : R)to(k : R).A ring has two casts,
NatCast.natCastandIntCast.intCast, and congruence only relates applications of the same function, so↑mand↑kstayed unrelated even whenm = ↑k. The ring solver now asserts((a : Int) : α) = ↑afor each cast↑aof a non-numeral fromNat, but only once the ring contains a cast of a non-numeral fromInt. The equation bypasses the normalizer, which would rewrite it to↑a = ↑a.🤖 Generated with Claude Code