95e532a536
This PR implements support for the heterogeneous `(k : Nat) * (a : R)` in ordered modules. Example: ```lean variable (R : Type u) [IntModule R] [LinearOrder R] [IntModule.IsOrdered R] example (x y z : R) (hx : x ≤ 3 * y) (h2 : y ≤ 2 * z) (h3 : x ≥ 6 * z) : x = 3 * y := by grind example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : x * y < 5) : ¬ 12*y - 4* z < 0 := by grind ```
24 lines
1.1 KiB
Text
24 lines
1.1 KiB
Text
open Lean.Grind
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-- `grind linarith` currently does not support negation of linear constraints.
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variable (R : Type u) [IntModule R] [Preorder R] [IntModule.IsOrdered R]
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example (a b : R) (_ : a < b) (_ : b < a) : False := by grind
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example (a b : R) (_ : a < b ∧ b < a) : False := by grind
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example (a b : R) (_ : a < b) : a ≠ b := by grind
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example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : 12 * y - 4 * z < 0) : False := by
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grind
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example (x y z : R) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : 12 * y - 4 * z < 0) : False := by
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grind
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example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : x * y < 5) (h3 : 12 * y - 4 * z < 0) :
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False := by grind
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example (x y z : R) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : 12 * y - 4 * z < 0) :
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False := by grind
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-- It does cancel the double negation in the following two examples
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example (x y z : Int) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) (h3 : x * y < 5) : ¬ 12*y - 4* z < 0 := by
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grind
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example (x y z : R) (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0) : ¬ 12 * y - 4 * z < 0 := by
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grind
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