reserve x for set;

theorem Th3:
  for L1, L2 being non empty 1-sorted st the carrier of L1 = the
  carrier of L2 for N1 being NetStr over L1 st N1 in NetUniv L1 ex N2 being
  strict net of L2 st N2 in NetUniv L2 & the RelStr of N1 = the RelStr of N2 &
  the mapping of N1 = the mapping of N2
proof
  let L1, L2 be non empty 1-sorted such that
A1: the carrier of L1 = the carrier of L2;
  let N1 be NetStr over L1;
  assume N1 in NetUniv L1;
  then consider N being strict net of L1 such that
A2: N = N1 & the carrier of N in the_universe_of the carrier of L1 by
YELLOW_6:def 11;
  reconsider f = the mapping of N as Function of the carrier of N, the carrier
  of L2 by A1;
  take NetStr(#the carrier of N, the InternalRel of N, f#);
  thus thesis by A1,A2,YELLOW_6:def 11;
end;
