2013-09-04 01:00:30 +00:00
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Theorem simple (p q r : Bool) : (p ⇒ q) ∧ (q ⇒ r) ⇒ p ⇒ r :=
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2013-09-04 12:39:35 +00:00
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Discharge (λ H_pq_qr, Discharge (λ H_p,
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let P_pq := Conjunct1 H_pq_qr,
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P_qr := Conjunct2 H_pq_qr,
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P_q := MP P_pq H_p
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in MP P_qr P_q))
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2013-09-04 01:00:30 +00:00
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Set pp::implicit true
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Show Environment 1
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2013-09-04 12:39:35 +00:00
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Theorem simple2 (a b c : Bool) : (a ⇒ b ⇒ c) ⇒ (a ⇒ b) ⇒ a ⇒ c :=
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Discharge (λ H_abc, Discharge (λ H_ab, Discharge (λ H_a,
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let P_b := (MP H_ab H_a),
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P_bc := (MP H_abc H_a)
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in MP P_bc P_b)))
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Show Environment 1
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