29 lines
1.1 KiB
Text
29 lines
1.1 KiB
Text
module
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open Lean Grind
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section CommSemiring
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variable (R : Type u) [CommSemiring R]
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example (a b c : R) : a * (b + c) = a * c + b * a := by grind
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example (a b : R) : (a + b)^2 = a^2 + 2 * a * b + b^2 := by grind
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example (a b : R) : (a + 2 * b)^2 = a^2 + 4 * a * b + 4 * b^2 := by grind
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example (a b : R) : (a + 2 * b)^2 = 4 * b^2 + b * 4 * a + a^2 := by grind
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example (a b : R) : (a + b)^2 ≠ a^2 + 2 * a * b + b^2 → False := by grind
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/--
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trace: [grind.debug.proof] fun h h_1 =>
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h_1
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(CommRing.eq_normS (RArray.branch 1 (RArray.leaf a) (RArray.leaf b))
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(((CommRing.Expr.var 0).add (CommRing.Expr.var 1)).pow 2)
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((((CommRing.Expr.var 0).pow 2).add
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(((CommRing.Expr.num 2).mul (CommRing.Expr.var 0)).mul (CommRing.Expr.var 1))).add
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((CommRing.Expr.var 1).pow 2))
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(eagerReduce (Eq.refl true)))
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-/
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#guard_msgs in -- context should contain only `a` and `b`
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set_option trace.grind.debug.proof true in
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example (a b c d : R) : c + d = d → (a + b)^2 ≠ a^2 + 2 * a * b + b^2 → False := by grind
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end CommSemiring
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