23 lines
648 B
Text
23 lines
648 B
Text
prelude definition bool : Type := Sort 0
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definition and (p q : bool) : bool := ∀ c : bool, (p → q → c) → c
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infixl ` ∧ `:25 := and
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constant a : bool
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-- Error
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theorem and_intro1 (p q : bool) (H1 : p) (H2 : q) : a
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:= fun (c : bool) (H : p -> q -> c), H H1 H2
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-- Error
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theorem and_intro2 (p q : bool) (H1 : p) (H2 : q) : p ∧ p
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:= fun (c : bool) (H : p -> q -> c), H H1 H2
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-- Error
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theorem and_intro3 (p q : bool) (H1 : p) (H2 : q) : q ∧ p
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:= fun (c : bool) (H : p -> q -> c), H H1 H2
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-- Correct
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theorem and_intro4 (p q : bool) (H1 : p) (H2 : q) : p ∧ q
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:= fun (c : bool) (H : p -> q -> c), H H1 H2
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#check and_intro4
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