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
```
131 lines
3.4 KiB
Text
131 lines
3.4 KiB
Text
set_option grind.debug true
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set_option warn.sorry false
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opaque op : Int → Int → Int
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instance : Std.Associative op := sorry
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local infixr:64 " ∘ " => op
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variable (a b c d e f g h i j k m n p q r s t u v w x y z : Int)
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example : ((a ∘ b) ∘ c) ∘ d = a ∘ (b ∘ (c ∘ d)) := by
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grind only
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example : (a ∘ (b ∘ c)) ∘ (d ∘ e) = a ∘ (b ∘ (c ∘ (d ∘ e))) := by
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grind only
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example (h₁ : a ∘ b = c ∘ d) : (x ∘ a) ∘ b ∘ y = x ∘ c ∘ d ∘ y := by
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grind only
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example (h₁ : a ∘ b = c ∘ d) (h₂ : b ∘ e = f ∘ g) :
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(c ∘ d) ∘ e = a ∘ (f ∘ g) := by
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grind only
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example (h₁ : b ∘ c = d ∘ e) (h₂ : a ∘ b = f ∘ g) :
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a ∘ (d ∘ e) = (f ∘ g) ∘ c := by
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grind only
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example
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(h₁ : a ∘ b = c ∘ d)
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(h₂ : b ∘ e = f ∘ g)
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(h₃ : e ∘ h = i ∘ j) :
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(c ∘ d) ∘ i ∘ j = a ∘ (f ∘ g) ∘ h := by
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grind only
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example
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(h₁ : b ∘ c = f ∘ g)
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(h₂ : e ∘ b = p ∘ q) :
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(p ∘ q) ∘ c = e ∘ (f ∘ g) := by
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grind only
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example
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(h₁ : a ∘ b = c ∘ d)
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(h₂ : e ∘ f = g ∘ h) :
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(c ∘ d) ∘ (e ∘ f) = a ∘ (b ∘ (g ∘ h)) := by
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grind only
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example
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(h₁ : u ∘ v = w ∘ x)
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(h₂ : v ∘ y = r ∘ s) :
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z ∘ (w ∘ x) ∘ y ∘ t = z ∘ u ∘ (r ∘ s) ∘ t := by
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grind only
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example
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(h₁ : a ∘ b = c ∘ d)
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(h₃ : b ∘ g = m ∘ n) :
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(c ∘ d) ∘ g = a ∘ (m ∘ n) := by
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grind only
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example
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(h₁ : a ∘ b = c ∘ d)
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(h₂ : d ∘ e = i ∘ j) :
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(a ∘ b) ∘ e = c ∘ (i ∘ j) := by
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grind only
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example
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(h₁ : a ∘ b = c ∘ d)
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(h₂ : b ∘ e = f ∘ g)
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(h₃ : g ∘ h = i ∘ j) :
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(c ∘ d) ∘ e ∘ h = a ∘ f ∘ (i ∘ j) := by
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grind only
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example
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: b ∘ e = f →
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a ∘ c = x ∘ y →
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b ∘ d = y ∘ z →
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x ∘ b ∘ d = a ∘ c ∘ z := by
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grind only
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example
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: x ∘ f = h →
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y ∘ g = i →
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a ∘ b = x ∘ x →
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b ∘ a = y ∘ y →
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x ∘ x ∘ a ∘ b ∘ x ∘ x = a ∘ y ∘ y ∘ y ∘ y ∘ b := by
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grind
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example
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: a ∘ b = x →
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b ∘ a = y →
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x ∘ a ∘ b ∘ x = a ∘ y ∘ y ∘ b := by
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grind
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example
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: a ∘ b = c →
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b ∘ a = d →
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c ∘ a ∘ b ∘ c = a ∘ d ∘ d ∘ b := by
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grind
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example {α} (op : α → α → α) [Std.Associative op] (a b c d : α)
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: op a b = c →
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op b a = d →
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op (op c a) (op b c) = op (op a d) (op d b) := by
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grind
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example {α} (op : α → α → α) [Std.Associative op] (u : α) [Std.LawfulIdentity op u] (a b c d : α)
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: op u (op a b) = op u c →
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op b (op a u) = op d u →
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op (op c a) (op (op b u) c) = op (op a d) (op d b) := by
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grind
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example {α} (f : α → α) (op : α → α → α) [Std.Associative op] (u : α) [Std.LawfulIdentity op u] (a b c d : α)
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: op u (op a b) = op u c →
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op b (op a u) = op d u →
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f (f (op (op c a) (op (op b u) c))) = f (f (op (op a d) (op d b))) := by
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grind
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example {α} (a b c d : List α)
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: a ++ b = c →
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b ++ a = d →
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c ++ a ++ b ++ c = a ++ d ++ d ++ b := by
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grind only
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example {α} (a b c d : List α)
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: a ++ b = c ++ c →
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b ++ a = d ++ d →
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c ++ c ++ a ++ b ++ c ++ c = a ++ d ++ d ++ d ++ d ++ b := by
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grind only
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example {α} (a b c d : List α)
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: a ++ b = c ++ [] ++ c →
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b ++ a = d ++ d →
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c ++ c ++ a ++ [] ++ b ++ c ++ c = a ++ d ++ [] ++ d ++ d ++ d ++ b := by
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grind only
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