
theorem Th8:
  for L being non empty multMagma, a, b being Element of L holds a
  *<*b*> = <*a*b*>
proof
  let L be non empty multMagma, a, b be Element of L;
A1: for i being object st i in dom<*b*> holds <*a*b*>/.i = a*(<*b*>/.i)
  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 <*a*b*>/.i = a*b by FINSEQ_4:16
      .= a*(<*b*>/.i) by A2,FINSEQ_4:16;
  end;
  dom<*a*b*> = Seg 1 by FINSEQ_1:38
    .= dom<*b*> by FINSEQ_1:38;
  hence thesis by A1,Def1;
end;
