reserve x,y,z for object, X for set, I for non empty set, i,j for Element of I,
    M0 for multMagma-yielding Function,
    M for non empty multMagma-yielding Function,
    M1, M2, M3 for non empty multMagma,
    G for Group-like multMagma-Family of I,
    H for Group-like associative multMagma-Family of I;

theorem
  FreeAtoms(X --> M1) = [: X, the carrier of M1 :]
proof
  Union disjoin Carrier(X --> M1)
     = Union disjoin(X --> the carrier of M1) by PRALG_1:16
    .= [: the carrier of M1, X :] by CARD_3:25;
  hence thesis by SYSREL:5;
end;
