24 lines
1.1 KiB
Text
24 lines
1.1 KiB
Text
prelude -- Correct version
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#check let bool := Sort 0,
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and (p q : bool) := ∀ c : bool, (p → q → c) → c,
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infixl `∧`:25 := and,
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and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ q
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:= λ (c : bool) (H : p → q → c), H H1 H2,
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and_elim_left (p q : bool) (H : p ∧ q) : p
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:= H p (λ (H1 : p) (H2 : q), H1),
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and_elim_right (p q : bool) (H : p ∧ q) : q
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:= H q (λ (H1 : p) (H2 : q), H2)
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in and_intro
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-- TODO(Leo): fix expected output as soon as elaborator starts #checking let-expression type again
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#check let bool := Sort 0,
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and (p q : bool) := ∀ c : bool, (p → q → c) → c,
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infixl `∧`:25 := and,
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and_intro (p q : bool) (H1 : p) (H2 : q) : q ∧ p
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:= λ (c : bool) (H : p → q → c), H H1 H2,
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and_elim_left (p q : bool) (H : p ∧ q) : p
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:= H p (λ (H1 : p) (H2 : q), H1),
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and_elim_right (p q : bool) (H : p ∧ q) : q
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:= H q (λ (H1 : p) (H2 : q), H2)
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in and_intro
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