
theorem Th14:
  for L being non empty 1-sorted, N being non empty NetStr over L
  for i being Element of N holds N|i is full SubNetStr of N
proof
  let L be non empty 1-sorted, N be non empty NetStr over L, i be Element of N;
A1: the mapping of N|i = (the mapping of N)|the carrier of N|i by Def7;
  the InternalRel of N|i = (the InternalRel of N)|_2 the carrier of N|i by Def7
;
  then
A2: the InternalRel of N|i c= the InternalRel of N by XBOOLE_1:17;
  the carrier of N|i c= the carrier of N by Th13;
  then N|i is SubRelStr of N by A2,YELLOW_0:def 13;
  then reconsider K = N|i as SubNetStr of N by A1,YELLOW_6:def 6;
  the InternalRel of K = (the InternalRel of N)|_2 the carrier of K by Def7;
  then K is full SubRelStr of N by YELLOW_0:def 14,YELLOW_6:def 6;
  hence thesis by YELLOW_6:def 7;
end;
