reserve X for non empty set;
reserve x for Element of X;
reserve d1,d2 for Element of X;
reserve A for BinOp of X;
reserve M for Function of [:X,X:],X;
reserve V for Ring;
reserve V1 for Subset of V;
reserve V for Algebra;
reserve V1 for Subset of V;
reserve MR for Function of [:REAL,X:],X;
reserve a for Real;

theorem Th7:
  RAlgebra X is RealLinearSpace
proof
  for v being VECTOR of RAlgebra X holds 1 * v = v by FUNCSDOM:12;
  hence thesis by Lm2;
end;
