 reserve i,j,n,k,l for Nat;
 reserve T,S,X,Y,Z for Subset of MC-wff;
 reserve p,q,r,t,F,H,G for Element of MC-wff;
 reserve s,U,V for MC-formula;
reserve f,g for FinSequence of [:MC-wff,Proof_Step_Kinds_IPC:];

theorem Th5:
  f is_a_proof_wrt_IPC X implies 1 <= len f
proof
  assume f is_a_proof_wrt_IPC X; then
  0+1 <= len f by NAT_1:13;
  hence thesis;
end;
