Generating an internally 4-connected binary matroid from another

We prove that if NN is an internally 4-connected proper minor of a weakly 4-connected binary matroid MM with |E(N)|≥7|E(N)|≥7, then either there exists a weakly 4-connected minor M′M′ of MM such that M′M′ has an NN-minor and 1≤|E(M)|−|E(M′)|≤21≤|E(M)|−|E(M′)|≤2, or one of MM and M∗M∗ is isomorphic to DnDn, Dn∖f1Dn∖f1, DnDn, or Dn∖f1Dn∖f1.