b0a12cb49f
This PR marks `Nat` power and divisibility theorems for `grind`. We use
the new `grind_pattern` constraints to control theorem instantiation.
Examples:
```lean
example {x m n : Nat} (h : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
grind
example (a m n o p : Nat) : a ∣ n → a ∣ m * n * o * p := by
grind
example {a b x m n : Nat}
: n > 0 → x = b * 4^m * a → a = 9^n → m > 0 → x % 6 = 0 := by
grind
example {a n : Nat}
: m > 4 → a = 2^(m^n) → a % 2 = 0 := by
grind
```
Closes #11515
Remark: We are adding support for installing extra theorems to `lia`
(aka `cutsat`). The example at #11515 can already be solved by `grind`
with this PR, but we still need to add the new theorems to the set for
`lia`.
cc @kim-em
66 lines
1.8 KiB
Text
66 lines
1.8 KiB
Text
example {x m n : Nat} (h : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind
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/--
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info: Try these:
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[apply] grind only [usr Nat.div_pow_of_pos, usr Nat.dvd_mul_right_of_dvd]
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[apply] grind =>
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instantiate only [usr Nat.div_pow_of_pos]
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instantiate only [usr Nat.dvd_mul_right_of_dvd]
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lia
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-/
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#guard_msgs in
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example {x m n : Nat} (h : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind?
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example {x m n : Nat} (h : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind only [usr Nat.div_pow_of_pos, usr Nat.dvd_mul_right_of_dvd]
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example {x m n : Nat} (h : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind =>
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instantiate only [usr Nat.div_pow_of_pos]
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instantiate only [usr Nat.dvd_mul_right_of_dvd]
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lia
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example {x m n : Nat} (h₁ : x = 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind
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example {x m n : Nat} (h₁ : x = 4 ^ m * n) : m > 0 → x % 4 = 0 := by
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grind
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example {x m n : Nat} (h₁ : x = n * 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind
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example {a b x m n : Nat} (h₁ : x = b * a * 4 ^ (m + 1) * n) : x % 4 = 0 := by
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grind
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example {a b x m n : Nat} (h₁ : x = b * 4 ^ m * a * 3 ^ n) : n > 0 → m > 0 → x % 12 = 0 := by
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grind
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example {a b x m n : Nat} (h₁ : x = b * 4 ^ m * a * 3 ^ n) : n > 0 → m > 0 → x % 6 = 0 := by
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grind
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example (m n : Nat) (h : 4 ∣ m) : 4 ∣ m * n := by
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grind
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example (a m n : Nat) (h : a ∣ m) : a ∣ m * n := by
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grind
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example (a m n o p : Nat) : a ∣ m → a ∣ m * n * o * p := by
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grind
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example {a b x m n : Nat}
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: x = b * 4 ^ m * a → a = 3^n → n > 0 → m > 0 → x % 12 = 0 := by
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grind
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example {a b x m n : Nat}
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: n > 0 → x = b * 4^m * a → a = 9^n → m > 0 → x % 6 = 0 := by
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grind
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example {a n : Nat}
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: a = 2^(3^n) → a % 2 = 0 := by
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grind
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example {a n : Nat}
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: m > 4 → a = 2^(m^n) → a % 2 = 0 := by
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grind
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