33 lines
1.3 KiB
Text
33 lines
1.3 KiB
Text
Import int.
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Definition double {A : Type} (f : A -> A) : A -> A := fun x, f (f x).
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Definition big {A : Type} (f : A -> A) : A -> A := (double (double (double (double (double (double (double f))))))).
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(**
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-- Tactic for trying to prove goal using Reflexivity, Congruence and available assumptions
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local congr_tac = Repeat(OrElse(apply_tac("Refl"), apply_tac("Congr"), assumption_tac()))
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-- Create an eager tactic that only tries to prove goal after unfolding everything
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eager_tac = Then(-- unfold homogeneous equality
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Try(unfold_tac("eq")),
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-- keep unfolding defintions above and beta-reducing
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Repeat(unfold_tac() .. Repeat(beta_tac())),
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congr_tac)
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-- The 'lazy' version tries first to prove without unfolding anything
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lazy_tac = OrElse(Then(Try(unfold_tac("eq")), congr_tac, now_tac()),
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eager_tac)
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**)
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Theorem T1 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = (big f b).
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eager_tac.
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done.
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Theorem T2 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = (big f b).
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lazy_tac.
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done.
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Theorem T3 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = ((double (double (double (double (double (double (double f))))))) b).
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lazy_tac.
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done.
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