
theorem Th27:
  for A being non empty AltCatStr, B being non empty SubCatStr of A,
  o being Object of B holds (incl B).o = o
proof
  let A be non empty AltCatStr, B be non empty SubCatStr of A,
  o be Object of B;
A1: [o,o] in [:the carrier of B,the carrier of B:] by ZFMISC_1:87;
  thus
  (incl B).o = ((id[:the carrier of B,the carrier of B:]).[o,o])`1 by Def28
    .= [o,o]`1 by A1,FUNCT_1:18
    .= o;
end;
