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 Th13:
  FreeAtoms(<*M1,M2*>) = [: {1}, the carrier of M1 :] \/
    [: {2}, the carrier of M2 :]
proof
  set S1 = [: the carrier of M1, {1} :], S2 = [: the carrier of M2, {2} :];
  Union disjoin Carrier <* M1, M2 *>
     = Union disjoin <* the carrier of M1, the carrier of M2 *> by PRALG_1:18
    .= Union <* S1, S2 *> by FINSEQ_3:161
    .= union rng <* S1, S2 *> by CARD_3:def 4
    .= union {S1, S2} by FINSEQ_2:127
    .= S1 \/ S2 by ZFMISC_1:75
    .= [: {1}, the carrier of M1 :]~ \/ S2 by SYSREL:5
    .= [: {1}, the carrier of M1 :]~ \/ [: {2}, the carrier of M2 :]~
      by SYSREL:5
    .= ([: {1}, the carrier of M1 :] \/ [: {2}, the carrier of M2 :])~
      by RELAT_1:23;
  hence thesis;
end;
