
theorem
  for L being complete non empty Poset for S being non empty full
  SubRelStr of L for X being Subset of S st "/\"(X,L) in the carrier of S holds
  "/\"(X,S) = "/\"(X,L)
proof
  let L be complete non empty Poset;
  let S be non empty full SubRelStr of L;
  let X be Subset of S such that
A1: "/\"(X,L) in the carrier of S;
  ex_inf_of X,L by Th17;
  hence thesis by A1,Th63;
end;
