let P be set ; :: thesis: for m1, m2 being marking of P holds (m1 + m2) - m1 = m2
let m1, m2 be marking of P; :: thesis: (m1 + m2) - m1 = m2
A1: m1 c= m1 + m2 by Th16;
let p be set ; :: 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 ((m1 + m2) - m1) . p = ((m1 + m2) . p) - (m1 . p) by A1, Def6
.= ((m1 . p) + (m2 . p)) - (m1 . p) by A2, Def5
.= m2 . p ;
hence p multitude_of = p multitude_of ; :: thesis: verum