33 lines
1.8 KiB
Text
33 lines
1.8 KiB
Text
let and_intro : ∀ (p q : Bool),
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p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q :=
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λ (p q : Bool) (H1 : p) (H2 : q) (c : Bool) (H : p → q → c),
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H H1 H2,
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and_elim_left : ∀ (p q : Bool),
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(λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → p :=
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λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
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H p (λ (H1 : p) (H2 : q), H1),
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and_elim_right : ∀ (p q : Bool),
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(λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → q :=
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λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
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H q (λ (H1 : p) (H2 : q), H2)
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in and_intro :
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∀ (p q : Bool),
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p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q
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let1.lean:17:20: error: type mismatch at application
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(λ (and_intro : ∀ (p q : Bool), p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) q p),
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let and_elim_left : ∀ (p q : Bool),
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(λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → p :=
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λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
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H p (λ (H1 : p) (H2 : q), H1),
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and_elim_right : ∀ (p q : Bool),
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(λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q → q :=
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λ (p q : Bool) (H : (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) p q),
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H q (λ (H1 : p) (H2 : q), H2)
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in and_intro)
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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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expected type:
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∀ (p q : Bool),
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p → q → (λ (p q : Bool), ∀ (c : Bool), (p → q → c) → c) q p
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given type:
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∀ (p q : Bool),
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p → q → (∀ (c : Bool), (p → q → c) → c)
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