author | haftmann |
Fri, 14 Jun 2019 08:34:28 +0000 | |
changeset 70347 | e5cd5471c18a |
parent 65449 | c82e63b11b8b |
child 76213 | e44d86131648 |
permissions | -rw-r--r-- |
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(* Title: ZF/ex/BinEx.thy |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright 1994 University of Cambridge |
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Examples of performing binary arithmetic by simplification. |
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*) |
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clarified main ZF.thy / ZFC.thy, and avoid name clash with global HOL/Main.thy;
wenzelm
parents:
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diff
changeset
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theory BinEx imports ZF begin |
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(*All runtimes below are on a 300MHz Pentium*) |
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lemma "#13 $+ #19 = #32" |
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by simp (*0 secs*) |
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lemma "#1234 $+ #5678 = #6912" |
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by simp (*190 msec*) |
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lemma "#1359 $+ #-2468 = #-1109" |
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by simp (*160 msec*) |
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lemma "#93746 $+ #-46375 = #47371" |
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by simp (*300 msec*) |
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lemma "$- #65745 = #-65745" |
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by simp (*80 msec*) |
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(* negation of ~54321 *) |
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lemma "$- #-54321 = #54321" |
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by simp (*90 msec*) |
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lemma "#13 $* #19 = #247" |
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by simp (*110 msec*) |
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lemma "#-84 $* #51 = #-4284" |
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by simp (*210 msec*) |
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(*The worst case for 8-bit operands *) |
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lemma "#255 $* #255 = #65025" |
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by simp (*730 msec*) |
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lemma "#1359 $* #-2468 = #-3354012" |
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by simp (*1.04 secs*) |
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(** Comparisons **) |
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lemma "(#89) $* #10 \<noteq> #889" |
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by simp |
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lemma "(#13) $< #18 $- #4" |
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by simp |
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lemma "(#-345) $< #-242 $+ #-100" |
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by simp |
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lemma "(#13557456) $< #18678654" |
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by simp |
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lemma "(#999999) $\<le> (#1000001 $+ #1) $- #2" |
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by simp |
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lemma "(#1234567) $\<le> #1234567" |
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by simp |
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(*** Quotient and remainder!! [they could be faster] ***) |
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lemma "#23 zdiv #3 = #7" |
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by simp |
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lemma "#23 zmod #3 = #2" |
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by simp |
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(** negative dividend **) |
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lemma "#-23 zdiv #3 = #-8" |
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by simp |
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lemma "#-23 zmod #3 = #1" |
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by simp |
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(** negative divisor **) |
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lemma "#23 zdiv #-3 = #-8" |
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by simp |
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lemma "#23 zmod #-3 = #-1" |
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by simp |
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(** Negative dividend and divisor **) |
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lemma "#-23 zdiv #-3 = #7" |
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by simp |
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lemma "#-23 zmod #-3 = #-2" |
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by simp |
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end |
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