82d90b4cdc
This PR adds a custom simproc to handle `Decidable.rec`, where we force the rewrite in the argument of the `Decidable` type, that normally is not rewritten due to being a subsingleton. Closes #12386
29 lines
759 B
Text
29 lines
759 B
Text
set_option cbv.warning false
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def minFacAux (n : Nat) : Nat → Nat
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| k =>
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if h : n < k * k then n
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else
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if h' : k ∣ n then k
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else
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have : k ≤ n := by have := Nat.le_mul_self k; omega
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minFacAux n (k + 2)
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termination_by k => n + 2 - k
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def Nat.minFac (n : Nat) : Nat :=
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if 2 ∣ n then 2 else minFacAux n 3
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def Nat.log (b n : Nat) : Nat :=
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if b ≤ 1 then 0 else (go b n).2 where
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go : Nat → Nat → Nat × Nat
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| _, 0 => (n, 0)
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| b, fuel + 1 =>
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if n < b then
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(n, 0)
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else
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let (q, e) := go (b * b) fuel
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if q < b then (q, 2 * e) else (q / b, 2 * e + 1)
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theorem test : ¬∃ k, k ≤ Nat.log 2 15 ∧ 0 < k ∧ 15 = Nat.minFac 15 ^ k := by
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apply of_decide_eq_true
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conv => lhs; cbv
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