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This PR implements grind propagators for Nat operators that have a simproc associated with them, but do not have any theory solver support. Examples:

example (a b : Nat) : a = 3 → b = 6 → a &&& b = 2 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ||| b = 7 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ^^^ b = 5 := by grind
example (a b : Nat) : a = 3 → b = 6 → a <<< b = 192 := by grind
example (a b : Nat) : a = 1135 → b = 6 → a >>> b = 17 := by grind

Closes #11498

This PR implements `grind` propagators for `Nat` operators that have a
simproc associated with them, but do not have any theory solver
support. Examples:

```lean
example (a b : Nat) : a = 3 → b = 6 → a &&& b = 2 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ||| b = 7 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ^^^ b = 5 := by grind
example (a b : Nat) : a = 3 → b = 6 → a <<< b = 192 := by grind
example (a b : Nat) : a = 1135 → b = 6 → a >>> b = 17 := by grind
```

Closes #11498
@leodemoura leodemoura added the changelog-tactics User facing tactics label Dec 5, 2025
@leodemoura leodemoura enabled auto-merge December 5, 2025 05:34
@leodemoura leodemoura added this pull request to the merge queue Dec 5, 2025
Merged via the queue into master with commit b3753ba Dec 5, 2025
19 checks passed
algebraic-dev pushed a commit that referenced this pull request Dec 8, 2025
This PR implements `grind` propagators for `Nat` operators that have a
simproc associated with them, but do not have any theory solver support.
Examples:

```lean
example (a b : Nat) : a = 3 → b = 6 → a &&& b = 2 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ||| b = 7 := by grind
example (a b : Nat) : a = 3 → b = 6 → a ^^^ b = 5 := by grind
example (a b : Nat) : a = 3 → b = 6 → a <<< b = 192 := by grind
example (a b : Nat) : a = 1135 → b = 6 → a >>> b = 17 := by grind
```

Closes #11498
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grind fails to reason on an arithmetic goal modulo an equality

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