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section "Common Basis Theory"
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theory Base_FDS
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imports "HOL-Library.Pattern_Aliases"
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begin
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declare Let_def [simp]
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text \<open>Lemma \<open>size_prod_measure\<close>, when declared with the \<open>measure_function\<close> attribute,
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enables \<open>fun\<close> to prove termination of a larger class of functions automatically.
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By default, \<open>fun\<close> only tries lexicographic combinations of the sizes of the parameters.
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With \<open>size_prod_measure\<close> enabled it also tries measures based on the sum of the sizes
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of different parameters.
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To alert the reader whenever such a more subtle termination proof is taking place
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the lemma is not enabled all the time but only when it is needed.
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\<close>
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lemma size_prod_measure:
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"is_measure f \<Longrightarrow> is_measure g \<Longrightarrow> is_measure (size_prod f g)"
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by (rule is_measure_trivial)
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end
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