14 lines
697 B
Text
14 lines
697 B
Text
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-- Basic (propositional) forward chaining
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constants (A B C D : Prop)
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definition lemma1 : A → (A → B) → B := by blast
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definition lemma2 : ¬ B → (A → B) → ¬ A := by blast
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definition lemma3 : ¬ C → A → (A → B → C) → ¬ B := by blast
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definition lemma4 : C → A → (A → B → ¬ C) → ¬ B := by blast
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-- TODO(dhs): [forward_action] is responsible for
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-- eliminating double negation
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definition lemma5 : C → A → (A → ¬ B → ¬ C) → ¬ ¬ B := by blast
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definition lemma6 : (A → B → ¬ C) → C → A → ¬ B := by blast
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definition lemma7 : ¬ C → (A → B → C) → A → ¬ B := by blast
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definition lemma8 : A → (A → B) → C → B ∧ C := by blast
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