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Author SHA1 Message Date
Leonardo de Moura
aaec0f584c
feat: ac normalization in grind (#10146)
This PR implements the basic infrastructure for the new procedure
handling AC operators in grind. It already supports normalizing
disequalities. Future PRs will add support for simplification using
equalities, and computing critical pairs. Examples:
```lean
example {α : Sort u} (op : α → α → α) [Std.Associative op] (a b c : α)
    : op a (op b c) = op (op a b) c := by
  grind only

example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.LawfulIdentity op u] (a b c : α)
    : op a (op b c) = op (op a b) (op c u) := by
  grind only

example {α : Type u} (op : α → α → α) (u : α) [Std.Associative op] [Std.Commutative op] 
    [Std.IdempotentOp op] [Std.LawfulIdentity op u] (a b c : α)
    : op (op a a) (op b c) = op (op (op b a) (op (op u b) b)) c := by
  grind only

example {α} (as bs cs : List α) : as ++ (bs ++ cs) = ((as ++ []) ++ bs) ++ (cs ++ []) := by
  grind only

example (a b c : Nat) : max a (max b c) = max (max b 0) (max a c) ∧ min a b = min b a := by
  grind only [cases Or]
```
2025-08-27 03:28:30 +00:00