lean2/tests/lean/bug1.lean

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definition bool [inline] : Type.{1} := Type.{0}
definition and [inline] (p q : bool) : bool := ∀ c : bool, (p → q → c) → c
infixl `∧` 25 := and
variable a : bool
-- Error
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : a
:= fun (c : bool) (H : p -> q -> c), H H1 H2
-- Error
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ p
:= fun (c : bool) (H : p -> q -> c), H H1 H2
-- Error
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : q ∧ p
:= fun (c : bool) (H : p -> q -> c), H H1 H2
-- Correct
theorem and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ q
:= fun (c : bool) (H : p -> q -> c), H H1 H2
check and_intro