let PTN be PT_net_Str ; :: thesis: *' ({} the Transitions of PTN) = {}
consider x being Element of *' ({} the Transitions of PTN);
assume not *' ({} the Transitions of PTN) = {} ; :: thesis: contradiction
then x in *' ({} the Transitions of PTN) ;
then ex s being place of PTN st
( x = s & ex f being S-T_arc of PTN ex t being transition of PTN st
( t in {} the Transitions of PTN & f = [s,t] ) ) ;
hence contradiction ; :: thesis: verum