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iehality committed Sep 5, 2024
1 parent 6b5e0b9 commit 773fd52
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5 changes: 3 additions & 2 deletions Incompleteness/Modal/Basic.lean
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import Incompleteness.DC.Basic
import Logic.Modal.Standard.Deduction
import Logic.Modal.Hilbert

namespace LO.Modal.Standard.Provability

Expand Down Expand Up @@ -91,6 +91,7 @@ lemma arithmetical_soundness_K4Loeb [π”Ÿ.HBL Tβ‚€ T] (h : πŠπŸ’(𝐋) ⊒! p
exact ihpq ⨀ ihp;
| _ => dsimp [interpretation]; trivial;

/-
theorem arithmetical_soundness_GL [π”Ÿ.HBL Tβ‚€ T] (h : 𝐆𝐋 ⊒! p) : βˆ€ {f : realization L Ξ±}, T ⊒!. (f[π”Ÿ] p) := by
apply arithmetical_soundness_K4Loeb (Tβ‚€ := Tβ‚€);
exact (System.weakerThan_iff.mp reducible_GL_K4Loeb) h;
Expand All @@ -109,7 +110,7 @@ lemma arithmetical_soundness_N [π”Ÿ.HBL Tβ‚€ T] (h : 𝐍 ⊒! p) : βˆ€ {f : re
simp only [interpretation] at ihpq;
exact ihpq ⨀ ihp;
| _ => dsimp [interpretation]; trivial;

-/
end ArithmeticalSoundness

end Modal.Standard.Provability
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4 changes: 2 additions & 2 deletions lake-manifest.json
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Expand Up @@ -75,7 +75,7 @@
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Expand All @@ -85,7 +85,7 @@
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"name": "arithmetization",
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"inputRev": "master",
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