reserve T for non empty RelStr,
  a for Element of T;
reserve a for set;
reserve P for non empty POSet_set,
  A,B for Element of P;

theorem Th10:
  MonFuncs (A,B) c= Funcs Carr P
proof
  reconsider CA = the carrier of A, CB = the carrier of B as Element of Carr P
  by Def7;
  let x be object;
  assume x in MonFuncs(A,B);
  then
A1: ex g be Function of A, B st x = g & g in Funcs (the carrier of A, the
  carrier of B) & g is monotone by Def6;
  Funcs (CA,CB) c= Funcs Carr P by ENS_1:2;
  hence thesis by A1;
end;
