a4f6f391fe
This PR implements equality propagation from the new AC module into the
`grind` core. Examples:
```lean
example {α β : Sort u} (f : α → β) (op : α → α → α) [Std.Associative op] [Std.Commutative op]
(a b c d : α) : op a (op b b) = op d c → f (op (op b a) (op b c)) = f (op c (op d c)) := by
grind only
example (a b c : Nat) : min a (max b (max c 0)) = min (max c b) a := by
grind -cutsat only
example {α β : Sort u} (bar : α → β) (op : α → α → α) [Std.Associative op] [Std.IdempotentOp op]
(a b c d e f x y w : α) :
op d (op x c) = op a b →
op e (op f (op y w)) = op (op d a) (op b c) →
bar (op d (op x c)) = bar (op e (op f (op y w))) := by
grind only
```
53 lines
2.3 KiB
Text
53 lines
2.3 KiB
Text
open Lean Grind AC
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example {α : Type u} (op : α → α → α) [Std.Associative op] (a b c : α)
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: op a (op b c) = op (op a b) c := by
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grind only
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example {α : Sort u} (op : α → α → α) [Std.Associative op] (a b c : α)
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: op a (op b c) = op (op a b) c := by
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grind only
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example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.LawfulIdentity op u] (a b c : α)
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: op a (op b c) = op (op a b) (op c u) := by
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grind only
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example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.Commutative op] (a b c : α)
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: op c (op b a) = op (op b a) c := by
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grind only
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example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.Commutative op] [Std.LawfulIdentity op u] (a b c : α)
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: op a (op b c) = op (op b a) c := by
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grind only
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example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.Commutative op] [Std.LawfulIdentity op u] (a b c : α)
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: op a (op b (op u c)) = op (op b a) (op u c) := by
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grind only
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example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.IdempotentOp op] (a b c : α)
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: op (op a a) (op b c) = op (op a (op b b)) c := by
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grind only
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example {α : Sort u} (op : α → α → α) [Std.Associative op] [Std.Commutative op] [Std.IdempotentOp op] (a b c : α)
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: op (op a a) (op b c) = op (op (op b a) (op b b)) c := by
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grind only
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example {α : Sort u} (op : α → α → α) (u : α) [Std.Associative op] [Std.Commutative op] [Std.IdempotentOp op] [Std.LawfulIdentity op u] (a b c : α)
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: op (op a a) (op b c) = op (op (op b a) (op (op u b) b)) c := by
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grind only
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example {α : Type u} (op : α → α → α) [Std.Associative op] [Std.Commutative op] [Std.IdempotentOp op] (a b c : α)
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: op (op a a) (op b c) = op (op (op b a) (op b b)) c := by
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grind only
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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)
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: op (op a a) (op b c) = op (op (op b a) (op (op u b) b)) c := by
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grind only
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example {α} (as bs cs : List α) : as ++ (bs ++ cs) = ((as ++ []) ++ bs) ++ (cs ++ []) := by
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grind only
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example (a b c : Nat) : max a (max b c) = max (max b 0) (max a c) := by
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grind only
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example (a b c : Nat) : max a (max b c) = max (max b 0) (max a c) ∧ min a b = min b a := by
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grind (splits := 0) only
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