reserve n,i,j,k,l for Nat;
reserve D for non empty set;
reserve c,d for Element of D;
reserve p,q,q9,r for FinSequence of D;

theorem
  len p = j+1+k implies ex q,r,c st len q = j & len r = k & p = q^<*c*>^ r
proof
  assume len p = j+1+k;
  then consider q9,r such that
A1: len q9 = j+1 and
A2: len r = k & p = q9^r by FINSEQ_2:23;
  consider q,c such that
A3: q9 = q^<*c*> by A1,FINSEQ_2:19;
  take q,r,c;
  len q9 = len q + 1 by A3,FINSEQ_2:16;
  hence thesis by A1,A2,A3;
end;
