equal
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362 |
362 |
363 apply(auto dest:not_in_lfp_afD); |
363 apply(auto dest:not_in_lfp_afD); |
364 done; |
364 done; |
365 |
365 |
366 text{* |
366 text{* |
367 The main theorem is proved as for PDL, except that we also derive the necessary equality |
367 If you found the above proofs somewhat complicated we recommend you read |
368 @{text"lfp(af A) = ..."} by combining @{thm[source]AF_lemma1} and @{thm[source]AF_lemma2} |
368 \S\ref{sec:CTL-revisited} where we shown how inductive definitions lead to |
369 on the spot: |
369 simpler arguments. |
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370 |
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371 The main theorem is proved as for PDL, except that we also derive the |
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372 necessary equality @{text"lfp(af A) = ..."} by combining |
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373 @{thm[source]AF_lemma1} and @{thm[source]AF_lemma2} on the spot: |
370 *} |
374 *} |
371 |
375 |
372 theorem "mc f = {s. s \<Turnstile> f}"; |
376 theorem "mc f = {s. s \<Turnstile> f}"; |
373 apply(induct_tac f); |
377 apply(induct_tac f); |
374 apply(auto simp add: EF_lemma equalityI[OF AF_lemma1 AF_lemma2]); |
378 apply(auto simp add: EF_lemma equalityI[OF AF_lemma1 AF_lemma2]); |