
theorem Th9:
  for L being non empty multMagma, a, b being Element of L holds
  <*b*>*a = <*b*a*>
proof
  let L be non empty multMagma, a, b be Element of L;
A1: for i being object st i in dom<*b*> holds <*b*a*>/.i = (<*b*>/.i)*a
  proof
    let i be object;
    assume i in dom<*b*>;
    then i in {1} by FINSEQ_1:2,38;
    then
A2: i = 1 by TARSKI:def 1;
    hence <*b*a*>/.i = b*a by FINSEQ_4:16
      .= (<*b*>/.i)*a by A2,FINSEQ_4:16;
  end;
  dom<*b*a*> = Seg 1 by FINSEQ_1:38
    .= dom<*b*> by FINSEQ_1:38;
  hence thesis by A1,Def2;
end;
