theorem
  F is_proper_subformula_of G '&' H implies F is_subformula_of G or F
  is_subformula_of H
proof
  assume
A1: F is_proper_subformula_of G '&' H;
A2: G '&' H is conjunctive;
  then
  the_left_argument_of (G '&' H) = G & the_right_argument_of (G '&' H) =H
  by Def19,Def20;
  hence thesis by A1,A2,Th38;
end;
