let P be set ; :: thesis: for m1, m2 being marking of P st m1 c= m2 holds
m2 = (m2 - m1) + m1
let m1, m2 be marking of P; :: thesis: ( m1 c= m2 implies m2 = (m2 - m1) + m1 )
assume A1: m1 c= m2 ; :: thesis: m2 = (m2 - m1) + m1
let p be object ; :: according to PNPROC_1:def 1 :: thesis: ( p in P implies p multitude_of = p multitude_of )
assume A2: p in P ; :: thesis: p multitude_of = p multitude_of
then ((m2 - m1) + m1) . p = ((m2 - m1) . p) + (m1 . p) by Def4
.= ((m2 . p) - (m1 . p)) + (m1 . p) by A1, A2, Def5
.= m2 . p ;
hence p multitude_of = p multitude_of ; :: thesis: verum