
theorem
  for L be unital non empty multMagma holds FPower(1_L,1) = id(the
  carrier of L)
proof
  let L be unital non empty multMagma;
A1: now
    let x be object;
    assume x in the carrier of L;
    then reconsider x1=x as Element of L;
    FPower(1_L,1).x1 = 1_L*power(x1,1) by Def12
      .= (power L).(x1,1) by GROUP_1:def 4;
    hence FPower(1_L,1).x = x by GROUP_1:50;
  end;
  dom FPower(1_L,1) = the carrier of L by FUNCT_2:def 1;
  hence thesis by A1,FUNCT_1:17;
end;
