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;
