from typing import Set

models = (
    {"a", "b", "c"},
)

DL_ATOMS = set.union(*models)

def propagate(atoms: Set[str]) -> Set[str]:
    atoms = atoms.intersection(DL_ATOMS)
    sub_models = (model for model in models if atoms <= model)
    first: set = next(sub_models, None)
    if first is None:
        return set()
    return first.intersection(*sub_models)

def check(atoms: Set[str]) -> bool:
    atoms = atoms.intersection(DL_ATOMS)
    return atoms in models