
theorem Th62:
  for S, T being non empty reflexive RelStr st the RelStr of S =
  the RelStr of T & S is /\-complete holds T is /\-complete
proof
  let S, T be non empty reflexive RelStr such that
A1: the RelStr of S = the RelStr of T and
A2: for X being non empty Subset of S ex x being Element of S st x
  is_<=_than X & for y being Element of S st y is_<=_than X holds x >= y;
  let X be non empty Subset of T;
  consider x being Element of S such that
A3: x is_<=_than X and
A4: for y being Element of S st y is_<=_than X holds x >= y by A1,A2;
  reconsider z = x as Element of T by A1;
  take z;
  thus z is_<=_than X by A1,A3,YELLOW_0:2;
  let y be Element of T;
  reconsider s = y as Element of S by A1;
  assume y is_<=_than X;
  then x >= s by A1,A4,YELLOW_0:2;
  hence thesis by A1,YELLOW_0:1;
end;
