let x1, x2, x3, x4 be Real; [*x1,x2,x3,x4*] *' = [*x1,(- x2),(- x3),(- x4)*]
set c = [*x1,x2,x3,x4*];
A1:
Rea [*x1,x2,x3,x4*] = x1
by QUATERNI:23;
A2:
Im1 [*x1,x2,x3,x4*] = x2
by QUATERNI:23;
A3:
Im2 [*x1,x2,x3,x4*] = x3
by QUATERNI:23;
Im3 [*x1,x2,x3,x4*] = x4
by QUATERNI:23;
hence
[*x1,x2,x3,x4*] *' = [*x1,(- x2),(- x3),(- x4)*]
by A1, A2, A3, QUATERNI:43; verum