reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;
reserve f,g for FinSequence of [:CQC-WFF(Al),Proof_Step_Kinds:];

theorem Th21:
  f is_a_proof_wrt X implies 1 <= len f
proof
  assume
 f is_a_proof_wrt X;
then A1: f <> {};
0+1 <= len f by A1,NAT_1:13;
  hence thesis;
end;
