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(* Title: HOL/AxClasses/Tutorial/Semigroups.thy
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ID: $Id$
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Author: Markus Wenzel, TU Muenchen
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Semigroups with different 'signatures'.
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*)
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Semigroups = HOL +
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consts
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"<+>" :: "['a, 'a] => 'a" (infixl 65)
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"<*>" :: "['a, 'a] => 'a" (infixl 70)
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assoc :: "(['a, 'a] => 'a) => bool"
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defs
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assoc_def "assoc f == ALL x y z. f (f x y) z = f x (f y z)"
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(* semigroups with op <+> *)
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axclass
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plus_sg < term
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plus_assoc "assoc (op <+>)"
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(* semigroups with op <*> *)
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axclass
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times_sg < term
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times_assoc "assoc (op <*>)"
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end
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