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SnO2WMaN committed Aug 27, 2024
1 parent 9865896 commit b9359b3
Showing 1 changed file with 3 additions and 3 deletions.
6 changes: 3 additions & 3 deletions Logic/Modal/Standard/PLoN/Semantics.lean
Original file line number Diff line number Diff line change
Expand Up @@ -305,7 +305,7 @@ lemma N4_characterized : ๐๐Ÿ’.CharacterizedByPLoNFrameClass (TransitiveFrame
exact validAxiomFour_of_transitive $ hTrans p (by simp_all);
| hMdp ihpq ihp => exact PLoN.ValidOnFrame.mdp ihpq ihp;
| hNec ihp => exact PLoN.ValidOnFrame.nec ihp;
| hOrElim => exact PLoN.ValidOnFrame.disjโ‚ƒ;
| hElimContra => exact PLoN.ValidOnFrame.elim_contra;
| _ => simp_all [PLoN.Satisfies];

lemma NRosser_characterized : ๐(๐‘).CharacterizedByPLoNFrameClass (SerialFrameClass ฮฑ) := by
Expand All @@ -321,7 +321,7 @@ lemma NRosser_characterized : ๐(๐‘).CharacterizedByPLoNFrameClass (SerialFr
exact PLoN.ValidOnFrame.nec ih;
. obtain โŸจp, eโŸฉ := hRosser; subst e; simp_all;
exact validRosserRule_of_serial (hSerial p (by simp_all)) ih;
| hOrElim => exact PLoN.ValidOnFrame.disjโ‚ƒ;
| hElimContra => exact PLoN.ValidOnFrame.elim_contra;
| _ => simp_all [PLoN.Satisfies];

-- TODO: `theory ๐๐Ÿ’ โˆช theory ๐(๐‘) = theory ๐๐Ÿ’(๐‘)`ใจใ„ใ†ไบ‹ๅฎŸใ‚’็คบใ›ใฐๅ…ฑ้€š้ƒจๅˆ†ใ ใ‘ใง็ฐกๅ˜ใซ็‰นๅพดใฅใ‘ใ‚‰ใ‚Œใ‚‹ๆฐ—ใŒใ™ใ‚‹
Expand All @@ -340,7 +340,7 @@ lemma N4Rosser_characterized : ๐๐Ÿ’(๐‘).CharacterizedByPLoNFrameClass (Tra
exact PLoN.ValidOnFrame.nec ih;
. obtain โŸจp, eโŸฉ := hRosser; subst e; simp_all;
exact validRosserRule_of_serial (hSerial (โ–กp) (by simp_all)) ih;
| hOrElim => exact PLoN.ValidOnFrame.disjโ‚ƒ;
| hElimContra => exact PLoN.ValidOnFrame.elim_contra;
| _ => simp_all [PLoN.Satisfies];


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