theorem
  dom(p - A) c= dom p
proof
A1: dom(p - A) = Seg len(p - A) by FINSEQ_1:def 3;
A2: dom p = Seg len p by FINSEQ_1:def 3;
  len(p - A) <= len p by Th58;
  hence thesis by A1,A2,FINSEQ_1:5;
end;
