Strong Completeness of Normal Modal Logic #15
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remain: lindenbaum, completeness_def
SnO2WMaN
commented
Jan 25, 2024
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レビュー終わり次第マージ可能です． |
iehality
approved these changes
Jan 29, 2024
Logic/Logic/HilbertStyle2.lean
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| @@ -3,99 +3,183 @@ import Logic.Logic.Calculus | |||
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| namespace LO | |||
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| class Deduction {F : Type u} [LogicSymbol F] (Bew : Set F → F → Sort*) where | |||
| axm : ∀ {f}, f ∈ T → Bew T f | |||
| class Deduction {F : Type u} [LogicSymbol F] (Bew : Finset F → F → Sort*) where | |||
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公理をFinsetではなく集合にしたほうが良いと思う（普通の導出関係を考えるならば同等のはずで、それならばより一般的な集合のほうが良いと思う）
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Hilbert流で最初からSetを許容すると，例えば演繹定理で
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それはおそらく次の補題を用いれば問題ないと思う.
証明で使用する公理は有限個なので帰納法で以下に相当する補題が証明できるはず
def Deduction.compact : T ⊢ p → (t : { t : Finset F // t ⊆ T }) × (t ⊢ p)
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TODO
completeness_def