theorem
  for x being set st x in dom Initialize p holds x in dom p or x = IC S
proof
  let x be set;
  assume
A1: x in dom Initialize p;
  dom Initialize p = dom p \/ {IC S} by Th42;
  then x in dom p or x in {IC S} by A1,XBOOLE_0:def 3;
  hence thesis by TARSKI:def 1;
end;
