reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem
  n = len p - card(p " A) implies dom(p - A) = Seg n
proof
  assume n = len p - card(p " A);
  then len(p - A) = n by Th57;
  hence thesis by FINSEQ_1:def 3;
end;
