theorem
  len fp = n+1 & a >= 1 & a <= n implies Del(fp,a).n = fp.(len fp)
proof
  assume that
A1: len fp = n+1 and
A2: a >= 1 and
A3: a <= n;
  n<n+1 by XREAL_1:29;
  then a<n+1 by A3,XXREAL_0:2;
  then a in dom fp by A1,A2,FINSEQ_3:25;
  hence thesis by A1,A3,WSIERP_1:def 1;
end;
