2014-06-20 18:27:30 +00:00
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definition bool [inline] : Type.{1} := Type.{0}
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2014-06-16 22:04:29 +00:00
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definition and (p q : bool) : bool
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:= ∀ c : bool, (p → q → c) → c
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2014-07-01 23:55:41 +00:00
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infixl `∧`:25 := and
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2014-06-16 22:04:29 +00:00
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theorem 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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theorem 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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theorem 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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theorem and_comm (p q : bool) (H : p ∧ q) : q ∧ p
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:= have H1 : p, from and_elim_left p q H,
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have H2 : q, from and_elim_right p q H,
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show q ∧ p, from and_intro q p H2 H1
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