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(* Title: HOL/AxClasses/Tutorial/BoolGroupInsts.thy
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ID: $Id$
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Author: Markus Wenzel, TU Muenchen
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Define overloaded constants "<*>", "inverse", "1" on type "bool"
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appropriately, then prove that this forms a group.
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*)
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BoolGroupInsts = Group +
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(* bool as abelian group *)
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defs
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prod_bool_def "x <*> y == x ~= (y::bool)"
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inverse_bool_def "inverse x == x::bool"
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unit_bool_def "1 == False"
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instance
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bool :: agroup {| ALLGOALS (fast_tac HOL_cs) |}
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(*"instance" automatically uses above defs,
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the remaining goals are proven 'inline'*)
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end
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