lean2/tests/lean/let1.lean

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prelude -- Correct version
check let bool := Type.{0},
and (p q : bool) := ∀ c : bool, (p → q → c) → c,
infixl `∧`:25 := and,
and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ q
:= λ (c : bool) (H : p → q → c), H H1 H2,
and_elim_left (p q : bool) (H : p ∧ q) : p
:= H p (λ (H1 : p) (H2 : q), H1),
and_elim_right (p q : bool) (H : p ∧ q) : q
:= H q (λ (H1 : p) (H2 : q), H2)
in and_intro
-- TODO(Leo): fix expected output as soon as elaborator starts checking let-expression type again
check let bool := Type.{0},
and (p q : bool) := ∀ c : bool, (p → q → c) → c,
infixl `∧`:25 := and,
and_intro [visible] (p q : bool) (H1 : p) (H2 : q) : q ∧ p
:= λ (c : bool) (H : p → q → c), H H1 H2,
and_elim_left (p q : bool) (H : p ∧ q) : p
:= H p (λ (H1 : p) (H2 : q), H1),
and_elim_right (p q : bool) (H : p ∧ q) : q
:= H q (λ (H1 : p) (H2 : q), H2)
in and_intro