theorem
  (non_op C)term a <> (ast C)term(b,t)
proof
  assume (non_op C)term a = (ast C)term(b,t);
  then (non_op C)term a = [ *, the carrier of C]-tree<*b,t*> by Th46;
  then ((non_op C)term a).{} = [ *, the carrier of C] by TREES_4:def 4;
  then ([non_op,the carrier of C]-tree<*a*>).{} = [ *, the carrier of C]
  by Th43;
  then [non_op, the carrier of C] = [ *, the carrier of C] by TREES_4:def 4;
  hence thesis by XTUPLE_0:1;
end;
