for F being Graph-yielding Function holds
( ( F is simple implies rng F is simple ) & ( rng F is simple implies F is simple ) & ( F is Dsimple implies rng F is Dsimple ) & ( rng F is Dsimple implies F is Dsimple ) & ( F is Tree-like implies rng F is Tree-like ) & ( rng F is Tree-like implies F is Tree-like ) )