66 lines
2.3 KiB
Standard ML
66 lines
2.3 KiB
Standard ML
open HolKernel Parse boolLib bossLib;
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val _ = new_theory "e2";
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val _ = Datatype `Philosopher = diogenes | platon | euklid`;
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val Philosopher_nchotomy = DB.fetch "-" "Philosopher_nchotomy";
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val Philosopher_distinct = DB.fetch "-" "Philosopher_distinct";
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val PHIL_KNOWLEDGE = new_specification ("PHIL_KNOWLEDGE", ["At", "Sp", "W", "B"],
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prove (``?At Sp W B.
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(!p. (Sp p ==> B p)) /\
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(!p. (At p ==> W p)) /\
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(!p. ~(Sp p) \/ ~(At p)) /\
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(!p. (Sp p) \/ (At p)) /\
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((Sp platon) ==> ~(W diogenes)) /\
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((Sp euklid) ==> ~(B diogenes)) /\
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((At diogenes) ==> ~(B euklid)) /\
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((At platon) ==> ~(W euklid))``,
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Q.EXISTS_TAC `\p. Philosopher_CASE p F F T` THEN
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Q.EXISTS_TAC `\p. Philosopher_CASE p T T F` THEN
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Q.EXISTS_TAC `\p. Philosopher_CASE p F T T` THEN
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Q.EXISTS_TAC `\p. Philosopher_CASE p T T F` THEN
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SIMP_TAC (srw_ss()++DatatypeSimps.expand_type_quants_ss [``:Philosopher``]) []));
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val PHIL_KNOWLEDGE_a = store_thm ("PHIL_KNOWLEDGE_a", ``!p. Sp p ==> B p``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_b = store_thm ("PHIL_KNOWLEDGE_b", ``!p. At p ==> W p``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_c = store_thm ("PHIL_KNOWLEDGE_b", ``!p. ~(Sp p) \/ ~(At p)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_c1 = store_thm ("PHIL_KNOWLEDGE_c1", ``!p. Sp p ==> ~(At p)``,
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PROVE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_c2 = store_thm ("PHIL_KNOWLEDGE_c2", ``!p. At p ==> ~(Sp p)``,
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PROVE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_d = store_thm ("PHIL_KNOWLEDGE_d", ``!p. (Sp p) \/ (At p)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_d1 = store_thm ("PHIL_KNOWLEDGE_d1", ``!p. ~(Sp p) ==> At p``,
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PROVE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_d2 = store_thm ("PHIL_KNOWLEDGE_d2", ``!p. ~(At p) ==> Sp p``,
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PROVE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_e = store_thm ("PHIL_KNOWLEDGE_e", ``(Sp platon) ==> ~(W diogenes)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_f = store_thm ("PHIL_KNOWLEDGE_f", ``(Sp euklid) ==> ~(B diogenes)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_g = store_thm ("PHIL_KNOWLEDGE_g", ``(At diogenes) ==> ~(B euklid)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val PHIL_KNOWLEDGE_h = store_thm ("PHIL_KNOWLEDGE_g", ``(At platon) ==> ~(W euklid)``,
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REWRITE_TAC[PHIL_KNOWLEDGE]);
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val _ = export_theory();
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