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 Th12:
  FreeAtoms(<*M1*>) = [: {1}, the carrier of M1 :]
proof
  Union disjoin Carrier <* M1 *>
     = Union disjoin <* the carrier of M1 *> by PRALG_1:17
    .= Union disjoin { [1, the carrier of M1] } by FINSEQ_1:def 5
    .= Union disjoin (1 .--> the carrier of M1) by FUNCT_4:82
    .= Union (1 .--> [: the carrier of M1, {1} :]) by CARD_3:4
    .= Union { [1, [: the carrier of M1, {1} :] ] } by FUNCT_4:82
    .= union rng { [1, [: the carrier of M1, {1} :] ] } by CARD_3:def 4
    .= union {[: the carrier of M1, {1} :]} by RELAT_1:9
    .= [: the carrier of M1, {1} :] by ZFMISC_1:25;
  hence thesis by SYSREL:5;
end;
