reserve k,n,m for Nat,
  a,x,X,Y for set,
  D,D1,D2,S for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for LTL-formula;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;

theorem
  (G is conjunctive or G is disjunctive or G is Until or G is Release )
  implies the_left_argument_of G is_subformula_of G & the_right_argument_of G
  is_subformula_of G
proof
  assume
A1: G is conjunctive or G is disjunctive or G is Until or G is Release;
  then the_right_argument_of G is_immediate_constituent_of G by Th22,Th23,Th24
,Th25;
  then
A2: the_right_argument_of G is_proper_subformula_of G by Th29;
  the_left_argument_of G is_immediate_constituent_of G by A1,Th22,Th23,Th24
,Th25;
  then the_left_argument_of G is_proper_subformula_of G by Th29;
  hence thesis by A2;
end;
