theorem Th13:
  q<>{} implies len (p^'q) +1 = len p + len q
proof
  set r = (p^'q);
  set qc = (2,len q)-cut q;
  assume q<>{};
  then 0+1<=len q by NAT_1:13;
  then 1+1<=len q +1 by XREAL_1:7;
  then
A1: len qc +(1+1) = len q + 1 by Lm2;
  thus len r +1 = len p + len qc + 1 by FINSEQ_1:22
    .= len p + len q by A1;
end;
