A1: Rea (<j> " ) = (Rea <j> ) / (|.<j> .| ^2 ) by QUATERN2:29
.= 0 by QUATERNI:31 ;
A2: Im1 (<j> " ) = - ((Im1 <j> ) / (|.<j> .| ^2 )) by QUATERN2:29
.= 0 by QUATERNI:31 ;
A3: Im2 (<j> " ) = - ((Im2 <j> ) / (|.<j> .| ^2 )) by QUATERN2:29
.= - 1 by QUATERNI:70, QUATERNI:31 ;
A4: Im3 (<j> " ) = - ((Im3 <j> ) / (|.<j> .| ^2 )) by QUATERN2:29
.= 0 by QUATERNI:31 ;
<j> " = [*(- 0 ),(- 0 ),(- 1),(- 0 )*] by A1, A2, A3, A4, QUATERNI:24
.= - <j> by QUATERN2:4 ;
hence <j> " = - <j> ; :: thesis: verum