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1 header{*Examples of Classical Reasoning*} |
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2 |
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3 theory FOL_examples imports "~~/src/FOL/FOL" begin |
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4 |
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5 lemma "EX y. ALL x. P(y)-->P(x)" |
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6 --{* @{subgoals[display,indent=0,margin=65]} *} |
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7 apply (rule exCI) |
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8 --{* @{subgoals[display,indent=0,margin=65]} *} |
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9 apply (rule allI) |
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10 --{* @{subgoals[display,indent=0,margin=65]} *} |
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11 apply (rule impI) |
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12 --{* @{subgoals[display,indent=0,margin=65]} *} |
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13 apply (erule allE) |
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14 --{* @{subgoals[display,indent=0,margin=65]} *} |
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15 txt{*see below for @{text allI} combined with @{text swap}*} |
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16 apply (erule allI [THEN [2] swap]) |
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17 --{* @{subgoals[display,indent=0,margin=65]} *} |
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18 apply (rule impI) |
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19 --{* @{subgoals[display,indent=0,margin=65]} *} |
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20 apply (erule notE) |
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21 --{* @{subgoals[display,indent=0,margin=65]} *} |
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22 apply assumption |
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23 done |
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24 |
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25 text {* |
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26 @{thm[display] allI [THEN [2] swap]} |
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27 *} |
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28 |
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29 lemma "EX y. ALL x. P(y)-->P(x)" |
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30 by blast |
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31 |
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32 end |
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33 |
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34 |
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