| author | wenzelm |
| Wed, 04 Oct 2017 12:00:53 +0200 | |
| changeset 66787 | 64b47495676d |
| parent 66453 | cc19f7ca2ed6 |
| child 67406 | 23307fd33906 |
| permissions | -rw-r--r-- |
| 58889 | 1 |
section{*Examples of Intuitionistic Reasoning*}
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session-qualified theory imports: isabelle imports -U -i -d '~~/src/Benchmarks' -a;
wenzelm
parents:
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changeset
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theory IFOL_examples imports IFOL begin |
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text{*Quantifier example from the book Logic and Computation*}
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lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))" |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule impI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule allI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule exI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule exE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule allE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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txt{*Now @{text "apply assumption"} fails*}
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oops |
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text{*Trying again, with the same first two steps*}
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lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))" |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule impI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule allI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule exE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule exI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule allE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply assumption |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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done |
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lemma "(EX y. ALL x. Q(x,y)) --> (ALL x. EX y. Q(x,y))" |
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by (tactic {*IntPr.fast_tac @{context} 1*})
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text{*Example of Dyckhoff's method*}
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lemma "~ ~ ((P-->Q) | (Q-->P))" |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (unfold not_def) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule impI) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule disj_impE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule imp_impE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (erule imp_impE) |
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply assumption |
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apply (erule FalseE)+ |
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done |
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end |