let r be Real; :: thesis: r * <e2> = |[0,r,0]|
( <e2> . 1 = 0 & <e2> . 2 = 1 & <e2> . 3 = 0 ) ;
then r * <e2> = |[(r * 0),(r * 1),(r * 0)]| by Lm1
.= |[0,r,0]| ;
hence r * <e2> = |[0,r,0]| ; :: thesis: verum