reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem
  q = p|(Seg i) implies len q = min(i,len p)
proof
  assume
A1: q = p|(Seg i);
  now
    per cases;
    case
      i <= len p;
      hence len q = i by A1,FINSEQ_1:17;
    end;
    case
      not i <= len p;
      hence len q = len p by A1,Th18;
    end;
  end;
  hence thesis by XXREAL_0:def 9;
end;
