17 lines
1.1 KiB
Text
17 lines
1.1 KiB
Text
-- Basic (propositional) forward chaining with conjunctive conclusions
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constants (a b c d e : nat)
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constants (p : nat → Prop)
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constants (q : nat → nat → Prop)
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constants (f : nat → nat)
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set_option blast.recursor false
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set_option blast.subst false
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definition lemma1 : a = d → b = e → p b → (p a → (¬ p e) ∧ p c) → ¬ p d := by blast
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definition lemma2a : ¬ p b → (p d → p b ∧ p c) → d = e → e = a → ¬ p a := by blast
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definition lemma2b : ¬ p (f b) → (p (f a) → p (f d) ∧ p (f c)) → b = d → ¬ p (f a) := by blast
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definition lemma3 : p (f (f b)) → (p (f a) → p (f c) ∧ (¬ p (f (f (f (f b)))))) → b = f b → ¬ p (f a) := by blast
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definition lemma4a : b = f b → ¬ p (f (f b)) → (p a → q c c ∧ p (f (f (f (f (f b)))))) → ¬ p a := by blast
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definition lemma4b : b = f b → ¬ p (f (f b)) → (p a → q c c ∧ q e c ∧ q d e ∧ p (f (f (f (f (f b))))) ∧ q e d) → ¬ p a :=
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by blast
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definition lemma5 : p b → (p (f a) → (¬ p b) ∧ p e ∧ p c) → ¬ p (f a) := by blast
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definition lemma6 : ¬ (q b a) → d = a → (p a → p e ∧ (q b d) ∧ p c) → ¬ p a := by blast
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