56 lines
948 B
Text
56 lines
948 B
Text
open nat tactic
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def g : nat → nat → nat :=
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λ x y, x * y
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def f : nat → nat
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| 0 := 10
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| (succ a) := g (f a) 2
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lemma ex0 (b a : nat) : b = f a → f (succ (succ a)) = g (g b 2) 2 :=
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begin
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intro h,
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simp [f],
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guard_target g (g (f a) 2) 2 = g (g b 2) 2,
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subst b
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end
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attribute [simp] f
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lemma ex1 (b a : nat) : b = f a → f (succ a) = g b 2 :=
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begin
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intro h,
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simp,
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guard_target g (f a) 2 = g b 2,
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subst b
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end
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lemma ex2 (b a : nat) : b = f a → f (succ (succ a)) = g (g b 2) 2 :=
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begin
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intro h,
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simp,
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guard_target g (g (f a) 2) 2 = g (g b 2) 2,
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subst b
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end
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local attribute [-simp] f
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lemma ex3 (b a : nat) : b = f a → f (succ a) = g b 2 :=
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begin
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intro h,
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fail_if_success {simp},
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subst b,
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reflexivity
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end
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run_cmd mk_simp_attr `mysimp
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attribute [mysimp] f
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lemma ex4 (b a : nat) : b = f a → f (succ a) = g b 2 :=
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begin
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intro h,
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simp with mysimp,
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guard_target g (f a) 2 = g b 2,
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subst b
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end
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