let L1, L2 be non empty 1-sorted ; :: thesis: ( the carrier of L1 = the carrier of L2 implies for N1 being NetStr over L1 ex N2 being strict NetStr over L2 st
( RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of N2, the InternalRel of N2 #) & the mapping of N1 = the mapping of N2 ) )

assume A1: the carrier of L1 = the carrier of L2 ; :: thesis: for N1 being NetStr over L1 ex N2 being strict NetStr over L2 st
( RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of N2, the InternalRel of N2 #) & the mapping of N1 = the mapping of N2 )

let N1 be NetStr over L1; :: thesis: ex N2 being strict NetStr over L2 st
( RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of N2, the InternalRel of N2 #) & the mapping of N1 = the mapping of N2 )

reconsider f = the mapping of N1 as Function of the carrier of N1, the carrier of L2 by A1;
take NetStr(# the carrier of N1, the InternalRel of N1,f #) ; :: thesis: ( RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of NetStr(# the carrier of N1, the InternalRel of N1,f #), the InternalRel of NetStr(# the carrier of N1, the InternalRel of N1,f #) #) & the mapping of N1 = the mapping of NetStr(# the carrier of N1, the InternalRel of N1,f #) )
thus ( RelStr(# the carrier of N1, the InternalRel of N1 #) = RelStr(# the carrier of NetStr(# the carrier of N1, the InternalRel of N1,f #), the InternalRel of NetStr(# the carrier of N1, the InternalRel of N1,f #) #) & the mapping of N1 = the mapping of NetStr(# the carrier of N1, the InternalRel of N1,f #) ) ; :: thesis: verum