equal
deleted
inserted
replaced
298 Goalw [increasing_def] |
298 Goalw [increasing_def] |
299 "F : increasing f ==> F : stable {s. z <= f s}"; |
299 "F : increasing f ==> F : stable {s. z <= f s}"; |
300 by (Blast_tac 1); |
300 by (Blast_tac 1); |
301 qed "increasingD"; |
301 qed "increasingD"; |
302 |
302 |
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303 Goalw [increasing_def, stable_def] "F : increasing (%s. c)"; |
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304 by Auto_tac; |
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305 qed "increasing_constant"; |
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306 AddIffs [increasing_constant]; |
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307 |
303 Goalw [increasing_def, stable_def, constrains_def] |
308 Goalw [increasing_def, stable_def, constrains_def] |
304 "mono g ==> increasing f <= increasing (g o f)"; |
309 "mono g ==> increasing f <= increasing (g o f)"; |
305 by Auto_tac; |
310 by Auto_tac; |
306 by (blast_tac (claset() addIs [monoD, order_trans]) 1); |
311 by (blast_tac (claset() addIs [monoD, order_trans]) 1); |
307 qed "mono_increasing_o"; |
312 qed "mono_increasing_o"; |