
theorem
  for L being non empty transitive RelStr
  for S being filtered-infs-inheriting non empty full SubRelStr of L
  for X being filtered Subset of S st X <> {} & ex_inf_of X,L
  holds ex_inf_of X,S & "/\"(X,S) = "/\"(X,L)
proof
  let L be non empty transitive RelStr;
  let S be filtered-infs-inheriting non empty full SubRelStr of L;
  let X be filtered Subset of S;
  assume that
A1: X <> {} and
A2: ex_inf_of X,L;
  "/\"(X,L) in the carrier of S by A1,A2,Def3;
  hence thesis by A2,YELLOW_0:63;
end;
