theorem Th14:
  seq(len g,len f) c= dom (g^f)
proof
    let a be object such that
A1: a in seq(len g,len f);
    reconsider n = a as Element of NAT by A1;
    n <= len f+len g by A1,Th1;
    then
A2: n <= len (g^f) by FINSEQ_1:22;
A3: 1 <= 1+len g by NAT_1:11;
    1+len g <= n by A1,Th1;
    then 1 <= n by A3,XXREAL_0:2;
    hence a in dom (g^f) by A2,FINSEQ_3:25;
end;
