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header{*Examples of Classical Reasoning*}
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theory FOL_examples = FOL:
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lemma "EX y. ALL x. P(y)-->P(x)"
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply (rule exCI)
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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 impI)
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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{*see below for @{text allI} combined with @{text swap}*}
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apply (erule allI [THEN [2] swap])
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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 notE)
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--{* @{subgoals[display,indent=0,margin=65]} *}
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apply assumption
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done
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text {*
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@{thm[display] allI [THEN [2] swap]}
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*}
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lemma "EX y. ALL x. P(y)-->P(x)"
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by blast
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end
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