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32556
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header {* Various examples for transfer procedure *}
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theory Transfer_Ex
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imports Complex_Main
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begin
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(* nat to int *)
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lemma ex1: "(x::nat) + y = y + x"
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by auto
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thm ex1 [transferred]
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lemma ex2: "(a::nat) div b * b + a mod b = a"
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by (rule mod_div_equality)
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thm ex2 [transferred]
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lemma ex3: "ALL (x::nat). ALL y. EX z. z >= x + y"
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by auto
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thm ex3 [transferred natint]
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lemma ex4: "(x::nat) >= y \<Longrightarrow> (x - y) + y = x"
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by auto
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thm ex4 [transferred]
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lemma ex5: "(2::nat) * (SUM i <= n. i) = n * (n + 1)"
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by (induct n rule: nat_induct, auto)
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thm ex5 [transferred]
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theorem ex6: "0 <= (n::int) \<Longrightarrow> 2 * \<Sum>{0..n} = n * (n + 1)"
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by (rule ex5 [transferred])
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thm ex6 [transferred]
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thm ex5 [transferred, transferred]
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end |