reserve X,Y for set;
reserve Z for non empty set;

theorem
  for A being non empty set, B,C being non empty Subset of A, D being
  non empty Subset of B st C=D holds incl C = incl B * incl D
proof
  let A be non empty set, B,C be non empty Subset of A, D be non empty Subset
  of B such that
A1: C=D;
  incl B * incl D = id (B /\ D) by FUNCT_1:22
    .= incl C by A1,XBOOLE_1:28;
  hence thesis;
end;
