db4206f2a9
This PR fixes an issue affecting `grind -revert`. In this mode, assigned metavariables in hypotheses were not being instantiated. This issue was affecting two files in Mathlib.
36 lines
1.1 KiB
Text
36 lines
1.1 KiB
Text
namespace Nat
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def ascFactorial (n : Nat) : Nat → Nat
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| 0 => 1
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| k + 1 => (n + k) * ascFactorial n k
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def descFactorial (n : Nat) : Nat → Nat
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| 0 => 1
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| k + 1 => (n - k) * descFactorial n k
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theorem descFactorial_of_lt {n : Nat} : ∀ {k : Nat}, n < k → n.descFactorial k = 0 := by sorry
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theorem add_descFactorial_eq_ascFactorial' (n : Nat) :
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∀ k : Nat, (n + k - 1).descFactorial k = n.ascFactorial k := by sorry
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def ascFactorialBinary (n k : Nat) : Nat :=
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match k with
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| 0 => 1
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| 1 => n
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| k@(_ + 2) => ascFactorialBinary n (k / 2) * ascFactorialBinary (n + k / 2) ((k + 1) / 2)
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theorem ascFactorial_eq_ascFactorialBinary : ascFactorial = ascFactorialBinary := sorry
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def descFactorialBinary (n k : Nat) : Nat :=
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if n < k then 0
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else ascFactorialBinary (n - k + 1) k
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theorem descFactorial_eq_descFactorialBinary : descFactorial = descFactorialBinary := by
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ext n k
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rw [descFactorialBinary]
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split <;> rename_i h
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· rw [descFactorial_of_lt h]
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· rw [← ascFactorial_eq_ascFactorialBinary, ← add_descFactorial_eq_ascFactorial']
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grind
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end Nat
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