
theorem
  for S be set, s be FinSequence of S, e be set st e in whole_event(s)
  ex x be Element of S st e in event_pick(x,s)
proof
  let S be set, s be FinSequence of S, e be set;
  assume
A1: e in whole_event(s);
  then e in s"S by RELSET_1:22;
  then s.e in S by FUNCT_1:def 7;
  then consider x be Element of S such that
A2: x=s.e;
  take x;
  x in {x} by TARSKI:def 1;
  hence thesis by A1,A2,FUNCT_1:def 7;
end;
