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;
reserve j for Nat;
reserve j1 for Element of NAT;

theorem
  F is_proper_subformula_of G 'R' H implies F is_subformula_of G or F
  is_subformula_of H
proof
  assume
A1: F is_proper_subformula_of G 'R' H;
  set G1 = G 'R' H;
A2: G1 is Release;
  then
A3: not G1 is Until by Lm21;
  ( not G1 is conjunctive)& not G1 is disjunctive by A2,Lm21;
  then the_left_argument_of G1 = G & the_right_argument_of G1 =H by A2,A3,Def19
,Def20;
  hence thesis by A1,A2,Th38;
end;
