d604c16c0e
This PR improves support for nonlinear `/` and `%` in `grind cutsat`. For example, given `a / b`, if `cutsat` discovers that `b = 2`, it now propagates that `a / b = b / 2`. This PR is similar to #9996, but for `/` and `%`. Example: ```lean example (a b c d : Nat) : b > 1 → d = 1 → b ≤ d + 1 → a % b = 1 → a = 2 * c → False := by grind ```
65 lines
2.1 KiB
Text
65 lines
2.1 KiB
Text
example (x y z w : Int) : z * x * y = 4 → x = z + w → z = 1 → w = 2 → False := by
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grind -ring
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example (x y z w : Int) : y * z * x = 4 → x = z + w → z = 1 → w = 2 → False := by
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grind -ring
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example (x y z w : Int) : y * z * x * w = 4 → x = 0 → False := by
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grind -ring
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example (x y z w : Int) : x = z + w → z = 1 → w = 2 → z * x * y = 4 → False := by
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grind -ring
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example (x y z : Int) : x = 3 → z = 1 → z * x * y = 4 → False := by
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grind -ring
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example (x y z w : Int) : x = 1 → y = 2 → z = 3 → w = 4 → x * y * z * w = 24 := by
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grind -ring
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example (x y z w : Int) : 1 ≤ x → x < 2 → y = 2 → z = 3 → w = 4 → x * y * z * w = 24 := by
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grind -ring
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example (x y z w : Int) : x = 1 → y = 2 → z = 3 → w = 4 → x * (y * z) * w = 24 := by
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grind -ring
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example (x y : Int) : 1 ≤ x → x ≤ 1 → 2 ≤ y → y ≤ 2 → x * y = 2 := by
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grind -ring
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example (a : Nat) (ha : a < 8) (b : Nat) (hb : b = 2) : a * b < 8 * b := by
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grind -ring
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example (a : Nat) (ha : a < 8) (b c : Nat) : 2 ≤ b → c = 1 → b ≤ c + 1 → a * b < 8 * b := by
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grind -ring
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example (h : s = 4) : 4 < s - 1 + (s - 1) * (s - 1 - 1) / 2 := by
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grind
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example (a b : Int) : a / b = 0 → b = 2 → a = 0 ∨ a = 1 := by
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grind
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example (a b : Int) : b = 2 → a / b = 0 → a = 0 ∨ a = 1 := by
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grind
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example (a b : Int) : b > 0 → b = 2 → a / b = 0 → a = 0 ∨ a = 1 := by
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grind
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example (a b : Nat) : b > 0 → b = 2 → a / b = 0 → a = 0 ∨ a = 1 := by
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grind
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example (a b c : Int) : a % b = 1 → b = 2 → a = 2 * c → False := by
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grind
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example (a b c : Int) : b = 2 → a % b = 1 → a = 2 * c → False := by
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grind
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example (a b c : Int) : b > 0 → b = 2 → a % b = 1 → a = 2 * c → False := by
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grind
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example (a b c : Nat) : b > 0 → b = 2 → a % b = 1 → a = 2 * c → False := by
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grind
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example (a b c d : Nat) : b > 0 → d = 1 → b = d + 1 → a % b = 1 → a = 2 * c → False := by
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grind
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example (a b c d : Nat) : b > 1 → d = 1 → b ≤ d + 1 → a % b = 1 → a = 2 * c → False := by
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grind
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