33 lines
879 B
Text
33 lines
879 B
Text
module
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variable (G : Type)
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structure G' where p : G
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@[ext, grind ext]
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theorem ext_ {f g : G' G} (h : f.p = g.p) : f = g := by
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cases f
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subst h
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rfl
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variable [Lean.Grind.IntModule G]
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instance : Add (G' G) where add f g := ⟨f.p + g.p⟩
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@[grind] theorem add_p (f g : G' G) : (f + g).p = f.p + g.p := rfl
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instance : Zero (G' G) where zero := ⟨0⟩
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@[grind] theorem zero_p : (0 : G' G).p = 0 := rfl
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instance : Neg (G' G) where neg x := ⟨-x.p⟩
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@[grind] theorem neg_p (f : G' G) : (-f).p = -(f.p) := rfl
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example (f g h : G' G) :
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f + g + h = f + (g + h) := by
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grind -- should work without extra options
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example (f g h : G' G) :
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f + g + h = f + (g + h) := by
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grind [Lean.Grind.AddCommMonoid.add_assoc] -- should work too
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example (f g h : G' G) :
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f + g + h = f + (g + h) := by
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grind -linarith [Lean.Grind.AddCommMonoid.add_assoc] -- should work too
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