reserve e for set;
reserve C,C1,C2,C3 for AltCatStr;
reserve C for non empty AltCatStr,
  o for Object of C;
reserve C for non empty transitive AltCatStr;

theorem Th28:
  for C being non empty AltCatStr, D being full non empty
  SubCatStr of C, o1,o2 being Object of C, p1,p2 being Object of D st o1 = p1 &
  o2 = p2 holds <^o1,o2^> = <^p1,p2^>
proof
  let C be non empty AltCatStr, D be full non empty SubCatStr of C, o1,o2 be
  Object of C, p1,p2 be Object of D such that
A1: o1 = p1 & o2 = p2;
  [p1,p2] in [:the carrier of D, the carrier of D:];
  hence <^o1,o2^> = ((the Arrows of C)||the carrier of D).(p1,p2) by A1,
FUNCT_1:49
    .= <^p1,p2^> by Def13;
end;
