| author | berghofe |
| Wed, 07 May 2008 10:57:19 +0200 | |
| changeset 26806 | 40b411ec05aa |
| parent 20550 | 5a925ad63f4d |
| permissions | -rw-r--r-- |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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(* Title: HOL/Complex/ex/BigO_Complex.thy |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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ID: $Id$ |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
diff
changeset
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Authors: Jeremy Avigad and Kevin Donnelly |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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*) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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header {* Big O notation -- continued *}
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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theory BigO_Complex |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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imports BigO Complex |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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begin |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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text {*
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Additional BigO lemmas that require the HOL-Complex logic image;
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Additional lemmas that require the \texttt{HOL-Complex} logic image.
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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*} |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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lemma bigo_LIMSEQ1: "f =o O(g) ==> g ----> 0 ==> f ----> (0::real)" |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (simp add: LIMSEQ_def bigo_alt_def) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply clarify |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (drule_tac x = "r / c" in spec) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (drule mp) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (erule divide_pos_pos) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply assumption |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply clarify |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (rule_tac x = no in exI) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (rule allI) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (drule_tac x = n in spec)+ |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (rule impI) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (drule mp) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply assumption |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (rule order_le_less_trans) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply assumption |
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Additional BigO lemmas that require the HOL-Complex logic image;
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apply (rule order_less_le_trans) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply (subgoal_tac "c * abs(g n) < c * (r / c)") |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply assumption |
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Additional BigO lemmas that require the HOL-Complex logic image;
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apply (erule mult_strict_left_mono) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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apply assumption |
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apply simp |
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done |
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lemma bigo_LIMSEQ2: "f =o g +o O(h) ==> h ----> 0 ==> f ----> a |
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==> g ----> (a::real)" |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (drule set_plus_imp_minus) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (drule bigo_LIMSEQ1) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply assumption |
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apply (simp only: fun_diff_def) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply (erule LIMSEQ_diff_approach_zero2) |
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ebd268806589
Additional BigO lemmas that require the HOL-Complex logic image;
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parents:
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apply assumption |
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parents:
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done |
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parents:
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parents:
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end |