reserve A for QC-alphabet;
reserve i,j,k,l,m,n for Nat;
reserve a,b,e for set;
reserve t,u,v,w,z for QC-symbol of A;
reserve p,q,r,s for Element of CQC-WFF(A);
reserve x for Element of bound_QC-variables(A);
reserve ll for CQC-variable_list of k,A;
reserve P for QC-pred_symbol of k,A;

theorem
  p is conjunctive implies ex q,r st p = q '&' r
proof
  assume p is conjunctive;
  then consider q, r being Element of QC-WFF(A) such that
A1: p = q '&' r by QC_LANG1:def 20;
A2: r is Element of CQC-WFF(A) by A1,CQC_LANG:9;
  q is Element of CQC-WFF(A) by A1,CQC_LANG:9;
  hence thesis by A1,A2;
end;
