
theorem Th25:
  for L be with_infima antisymmetric transitive RelStr for S be
  non empty meet-closed Subset of L holds subrelstr S is with_infima
proof
  let L be with_infima antisymmetric transitive RelStr;
  let S be non empty meet-closed Subset of L;
  subrelstr S is non empty meet-inheriting full SubRelStr of L by Def1;
  hence thesis;
end;
