
theorem Th28:
  for A being non empty AltCatStr, B being non empty SubCatStr of A,
  o1,o2 being Object of B holds <^o1,o2^> c= <^(incl B).o1,(incl B).o2^>
proof
  let A be non empty AltCatStr, B be non empty SubCatStr of A,
  o1,o2 be Object of B;
A1: [o1,o2] in [:the carrier of B,the carrier of B:] by ZFMISC_1:87;
A2: <^o1,o2^> = (the Arrows of B).(o1,o2) by ALTCAT_1:def 1
    .= (the Arrows of B).[o1,o2];
A3: (incl B).o1 = o1 by Th27;
  (incl B).o2 = o2 by Th27;
  then
A4: <^(incl B).o1,(incl B).o2^> = (the Arrows of A).(o1,o2) by A3,
ALTCAT_1:def 1
    .= (the Arrows of A).[o1,o2];
  the Arrows of B cc= the Arrows of A by ALTCAT_2:def 11;
  hence thesis by A1,A2,A4,ALTCAT_2:def 2;
end;
