theorem Th34:
  x in rng p implies len(p -| x) = x..p - 1
proof
  assume
A1: x in rng p;
  then consider n such that
A2: n = x..p - 1 and
A3: p | Seg n = p -| x by Def5;
A4: n <= n + 1 by NAT_1:12;
  n + 1 <= len p by A1,A2,Th21;
  then n <= len p by A4,XXREAL_0:2;
  hence thesis by A2,A3,FINSEQ_1:17;
end;
