let X, Y be set ; ( X misses Y implies ( the carrier of (PTempty_f_net X,Y) = X & the carrier' of (PTempty_f_net X,Y) = Y & Flow (PTempty_f_net X,Y) = {} ) )
assume
X misses Y
; ( the carrier of (PTempty_f_net X,Y) = X & the carrier' of (PTempty_f_net X,Y) = Y & Flow (PTempty_f_net X,Y) = {} )
then
PTempty_f_net X,Y = PT_net_Str(# X,Y,({} X,Y),({} Y,X) #)
by Def4;
hence
( the carrier of (PTempty_f_net X,Y) = X & the carrier' of (PTempty_f_net X,Y) = Y & Flow (PTempty_f_net X,Y) = {} )
; verum