theorem Th199: :: GLENUM00:199

for G being _Graph holds
( ( G is loopless implies G .allComponents() is loopless ) & ( G .allComponents() is loopless implies G is loopless ) & ( G is non-multi implies G .allComponents() is non-multi ) & ( G .allComponents() is non-multi implies G is non-multi ) & ( G is non-Dmulti implies G .allComponents() is non-Dmulti ) & ( G .allComponents() is non-Dmulti implies G is non-Dmulti ) & ( G is simple implies G .allComponents() is simple ) & ( G .allComponents() is simple implies G is simple ) & ( G is Dsimple implies G .allComponents() is Dsimple ) & ( G .allComponents() is Dsimple implies G is Dsimple ) & ( G is acyclic implies G .allComponents() is acyclic ) & ( G .allComponents() is acyclic implies G is acyclic ) & ( G is edgeless implies G .allComponents() is edgeless ) & ( G .allComponents() is edgeless implies G is edgeless ) & ( G is chordal implies G .allComponents() is chordal ) & ( G .allComponents() is chordal implies G is chordal ) & ( G is loopfull implies G .allComponents() is loopfull ) & ( G .allComponents() is loopfull implies G is loopfull ) )