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 universal implies ex x,q st p = All(x,q)
proof
  assume p is universal;
  then consider x being bound_QC-variable of A,
       q being Element of QC-WFF(A) such that
A1: p = All(x,q) by QC_LANG1:def 21;
  q is Element of CQC-WFF(A) by A1,CQC_LANG:13;
  hence thesis by A1;
end;
