61 lines
1.9 KiB
Text
61 lines
1.9 KiB
Text
reset_grind_attrs%
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def Set (α : Type) := α → Bool
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def insertElem [DecidableEq α] (s : Set α) (a : α) : Set α :=
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fun x => a = x || s x
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def contains (s : Set α) (a : α) : Bool :=
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s a
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namespace Set
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theorem contains_insert [DecidableEq α] (s : Set α) (a : α) : contains (insertElem s a) a := by
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simp [contains, insertElem]
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scoped grind_pattern contains_insert => contains (insertElem s a) a
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end Set
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
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fail_if_success grind -- should fail
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open Set in grind -- scoped pattern was activated, it should work now
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
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fail_if_success grind -- should fail
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intros; subst s₂ a₁; apply Set.contains_insert
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open Set in
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
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grind -- should work
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example [DecidableEq α] (s₁ s₂ : Set α) (a₁ a₂ : α) :
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s₂ = insertElem s₁ a₁ → a₁ = a₂ → contains s₂ a₂ := by
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fail_if_success grind -- should fail
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intros; subst s₂ a₁; apply Set.contains_insert
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-- TheoremPattern activation test
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def a := 10
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def b := 20
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def foo (x : List Nat) (y : List Nat) := x ++ y ++ x
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theorem fooThm : foo x [a, b] = x ++ [a, b] ++ x := rfl
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section
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local grind_pattern fooThm => foo x [a, b]
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/-- trace: [grind.ematch.instance] fooThm: foo x [a, b] = x ++ [a, b] ++ x -/
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#guard_msgs in
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set_option trace.grind.ematch.instance true in
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example : xs = [a, b] → foo x xs = x ++ [a, b] ++ x := by
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grind
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end
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example : xs = [a, b] → foo x xs = x ++ [a, b] ++ x := by
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fail_if_success grind -- should fail, `local grind_pattern` is not active anymore
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intro; subst xs; apply fooThm
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