reconsider jj = 1 as Element of REAL by NUMBERS:19;
let x, y be Element of REAL ; ( not * (x,y) = 0 or x = 0 or y = 0 )
assume that
A1:
* (x,y) = 0
and
A2:
x <> 0
; y = 0
A3:
* (x,(inv x)) = 1
by A2, Def4;
thus y =
* (jj,y)
by Th19
.=
* ((* (x,y)),(inv x))
by A3, Th13
.=
0
by A1, Th12
; verum