55d5ace68e
This PR tries to improve the E-matching pattern inference for `grind`. That said, we still need better tools for annotating and maintaining `grind` annotations in libraries. closes #9125
20 lines
783 B
Text
20 lines
783 B
Text
variable {R : Type} [Lean.Grind.CommRing R]
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-- My real code uses CommRing from Mathlib instead, and sees the same behavior.
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def P : Nat → R → R → R
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| 0, _, _ => 1
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| n+1, x, y => (x + y - 1) * (y + 1) * P n x (y + 2) + (y - y^2) * P n x y
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def S : Nat → R → R → R
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| n, x, y => ((x + y)^2 - 1) * (y + 1) * (x + 1) * P n (y + 2) (x + 2)
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theorem foo (n : Nat)
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(ih : ∀ m < n + 1 + 1, ∀ (x y : R), P m x y = P m y x)
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(h2 :
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∀ (x y : R),
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(x + y - 1) * (y + 1) * P n.succ (y + 2) x =
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S n x y + (x + y - 1) * (y + 1) * (x - x ^ 2) * P n (y + 2) x)
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(m : Nat) (hm : m < n.succ.succ) (x y : R) :
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((x + y) ^ 2 - 1) * (y + 1) * (x + 1) * P m (y + 2) (x + 2) =
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((y + x) ^ 2 - 1) * (x + 1) * (y + 1) * P m (x + 2) (y + 2) := by
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grind
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