reserve Y for non empty set;
reserve B for Subset of Y;

theorem
  for a,b,c being Function of Y,BOOLEAN
   holds a 'or' b 'or' c = a 'or' (b 'or' c)
proof
  let a,b,c be Function of Y,BOOLEAN;
  let x be Element of Y;
  thus (a 'or' b 'or' c).x = (a 'or' b).x 'or' c.x by Def4
     .= a.x 'or' b.x 'or' c.x by Def4
     .= a.x 'or' (b.x 'or' c.x)
     .= a.x 'or' (b 'or' c).x by Def4
     .= (a 'or' (b 'or' c)).x by Def4;
end;
