set I = the carrier of R;
set M = finite-MultiSet_over the carrier of R;
defpred S1[ bag of the carrier of R, bag of the carrier of R] means [(OrderedPartition $1),(OrderedPartition $2)] in LexOrder ( the carrier of (PrecM R), the InternalRel of (PrecM R));
consider N being strict RelExtension of finite-MultiSet_over the carrier of R such that
A1:
for m, n being Element of N holds
( m <= n iff S1[m,n] )
from BAGORD_2:sch 1();
take
N
; for m, n being Element of N holds
( m <= n iff [(OrderedPartition m),(OrderedPartition n)] in LexOrder ( the carrier of (PrecM R), the InternalRel of (PrecM R)) )
thus
for m, n being Element of N holds
( m <= n iff [(OrderedPartition m),(OrderedPartition n)] in LexOrder ( the carrier of (PrecM R), the InternalRel of (PrecM R)) )
by A1; verum