14 lines
852 B
Text
14 lines
852 B
Text
let bool : Type := Prop,
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and : bool → bool → Prop := λ (p q : bool), Π (c : bool), (p → q → c) → c,
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and_intro : Π (p q : bool), p → q → and p q :=
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λ (p q : bool) (H1 : p) (H2 : q) (c : bool) (H : p → q → c), H H1 H2,
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and_elim_left : Π (p q : bool), and p q → p := λ (p q : bool) (H : and p q), H p (λ (H1 : p) (H2 : q), H1),
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and_elim_right : Π (p q : bool), and p q → q := λ (p q : bool) (H : and p q), H q (λ (H1 : p) (H2 : q), H2)
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in and_intro :
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∀ (p q : Prop), p → q → ∀ (c : Prop), (p → q → c) → c
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let1.lean:19:17: error: invalid let-expression, expression
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λ (p q : bool) (H1 : p) (H2 : q) (c : bool) (H : p → q → c), H H1 H2
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has type
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Π (p q : bool), p → q → Π (c : bool), (p → q → c) → c
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but is expected to have type
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Π (p q : bool), p → q → and q p
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