reserve i, I for set,
  f, g, h for Function,
  s for ManySortedSet of I;

theorem Th22:
  for G1, G2, G3 being non empty multMagma holds
    <*G1,G2,G3*> is multMagma-Family of {1,2,3}
proof
  let G1, G2, G3 be non empty multMagma;
 dom <*G1,G2,G3*> = {1,2,3} by FINSEQ_1:89,FINSEQ_3:1;
  then reconsider A = <*G1,G2,G3*> as ManySortedSet of {1,2,3} by
PARTFUN1:def 2,RELAT_1:def 18;
  A is multMagma-yielding
  proof
    let y be set;
    assume y in rng A;
    then consider x being object such that
A1: x in dom A and
A2: A.x = y by FUNCT_1:def 3;
    x = 1 or x = 2 or x = 3 by A1,ENUMSET1:def 1;
    hence thesis by A2;
  end;
  hence thesis;
end;
