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30 lines
734 B
Text
30 lines
734 B
Text
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/- Chapter 3 — solutions. Term mode only, as required. -/
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namespace Ch03
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variable (P Q R : Prop)
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theorem const_imp : P → Q → P :=
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fun p _ => p
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theorem and_to_or : P ∧ Q → P ∨ Q :=
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fun h => Or.inl h.1
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theorem modus_ponens : P → (P → Q) → Q :=
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fun p f => f p
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theorem and_assoc' : (P ∧ Q) ∧ R → P ∧ (Q ∧ R) :=
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fun h => And.intro h.1.1 (And.intro h.1.2 h.2)
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theorem or_swap : P ∨ Q → Q ∨ P :=
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fun h => match h with
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| Or.inl p => Or.inr p
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| Or.inr q => Or.inl q
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/- The program: "given evidence p for P and a refuter f of P, feed p to f."
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A proof of ¬¬P is a function that defeats any would-be refutation. -/
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theorem not_not_intro : P → ¬¬P :=
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fun p f => f p
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end Ch03
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