reserve UA for Universal_Algebra,
  f, g for Function of UA, UA;
reserve I for set,
  A, B, C for ManySortedSet of I;

theorem Th11:
  for x be set, A be ManySortedSet of {x} holds A = x .--> A.x
proof
  let x be set;
  let A be ManySortedSet of {x};
A1: dom A = {x} by PARTFUN1:def 2;
  then rng A = {A.x} by FUNCT_1:4;
  hence thesis by A1,FUNCOP_1:9;
end;
