let x, y, z be ExtReal; ( x is real implies x * (y - z) = (x * y) - (x * z) )
assume
x is real
; x * (y - z) = (x * y) - (x * z)
then x * (y - z) =
(x * y) + (x * (- z))
by Th95
.=
(x * y) + (- (x * z))
by Th92
;
hence
x * (y - z) = (x * y) - (x * z)
; verum