reserve M for finite-degree Matroid,
  A,B,C for Subset of M,
  e,f for Element of M;

theorem Th39:
  A is cycle implies Rnk A + 1 = card A
proof
  assume
A1: A is cycle;
  then reconsider A as non empty finite Subset of M;
  set a = the Element of A;
A2: A\{a} is_maximal_independent_in A by A1,Th38;
A3: Rnk A = card (A\{a}) by A2,Th19;
  a in {a} by TARSKI:def 1;
  then
A4: a nin A\{a} by XBOOLE_0:def 5;
  A = (A\{a})\/{a} by ZFMISC_1:116;
  hence thesis by A3,A4,CARD_2:41;
end;
