theorem Th97:
  variables_in ((ast C)term(a,t)) = (variables_in a)\/(variables_in t)
proof
  (ast C)term(a,t) = [ *, the carrier of C]-tree <*a,t*> by Th46;
  then variables_in ((ast C)term(a,t))
  = ((C variables_in a)(\/)(C variables_in t)).a_Term by Th96;
  hence thesis by PBOOLE:def 4;
end;
