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;
reserve f,h for Element of Funcs(bound_QC-variables(A),bound_QC-variables(A)),
  K,L for Element of Fin bound_QC-variables(A);

theorem Th42:
  [q,t,K,f] in SepQuadruples p & x.u in f.:still_not-bound_in q implies u<t
proof
  assume that
A1: [q,t,K,f] in SepQuadruples p and
A2: x.u in f.:still_not-bound_in q;
  f.:still_not-bound_in q c= f.: (still_not-bound_in p \/ K) by A1,Th38,
RELAT_1:123;
  then x.u in f.:(still_not-bound_in p \/ K) by A2;
  then x.u in f.:still_not-bound_in p \/ f.:K by RELAT_1:120;
  then x.u in f.:still_not-bound_in p or x.u in f.:K by XBOOLE_0:def 3;
  hence thesis by A1,Th39,Th41;
end;
