
theorem P5a:
for F being Field,
    a being Element of F,
    b being non zero Element of F holds (a / b)^2 = (a^2) / (b^2)
proof
let F be Field; let a be Element of F, b be non zero Element of F;
H1: b <> 0.F;
thus (a / b)^2 = a * (b" * (a * b")) by GROUP_1:def 3
              .= a * (a * (b" * b")) by GROUP_1:def 3
              .= (a * a) * (b" * b") by GROUP_1:def 3
              .= (a^2) / (b^2) by VECTSP_2:11,H1;
end;
