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