reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;

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;
