| author | haftmann |
| Wed, 02 Jan 2008 15:14:20 +0100 | |
| changeset 25765 | 49580bd58a21 |
| parent 19469 | 958d2f2dd8d4 |
| permissions | -rw-r--r-- |
| 19358 | 1 |
(* Title: HOL/Complex/ex/Arithmetic_Series_Complex |
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ID: $Id$ |
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Author: Benjamin Porter, 2006 |
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*) |
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header {* Arithmetic Series for Reals *}
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theory Arithmetic_Series_Complex |
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19469
958d2f2dd8d4
moved arithmetic series to geometric series in SetInterval
kleing
parents:
19358
diff
changeset
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imports Complex_Main |
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begin |
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lemma arith_series_real: |
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"(2::real) * (\<Sum>i\<in>{..<n}. a + of_nat i * d) =
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of_nat n * (a + (a + of_nat(n - 1)*d))" |
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proof - |
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have |
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"((1::real) + 1) * (\<Sum>i\<in>{..<n}. a + of_nat(i)*d) =
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of_nat(n) * (a + (a + of_nat(n - 1)*d))" |
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by (rule arith_series_general) |
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thus ?thesis by simp |
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qed |
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end |