No. The two power supplies will behave exactly like the two LM317s.

Have you looked at the standard LM317 configuration? There two resistors in series across the output. The junction of these is fed back to an input of an internal differential opamp. The other input of the of opamp is an internal reference. The output of the opamp drives the internal pass transistor. If the output voltage is higher than the desired voltage, the voltage at the resistors' junction will be higher than the reference voltage and the opamp will reduce the drive to the pass transistor. This will continue until the voltage at the output matches the sensed voltage with the reference voltage. Lab supplies work the same. Since the 5v supply holds the top of the 4V regulator's series resistors at 5V, the 4V regulator reduces its pass transistor drive to cutoff in a futile attempt to sense 4V.

Ken

Yeah I think Mark set me straight by saying that the supply wpuld have to be able to 'SINK' current.

Thanks for your response too Ken.

 

........................ In order for this to happen the 4 volt regulator would have to sink current as well as source current. That is not how they are built. Every simple linear regulator I know of can only source current. .................

They are rare but there are a few, such as the LT1118, which can both sink and source current. They are designed for terminations, such as SCSI lines, that require both source and sink current, but can also be used as a general purpose regulator. One interesting application is to use two to make a dual regulated split supply from a single voltage (pseudo ground) that can be unbalanced by as much as 800mA in current draw between the two voltage splits.