Does anyone recognise this?

[A E Lawrence <A.E.Lawrence@xxxxxxxxxxx>]

In some work on priority, I have defined a "layered" partial order relation as
one for which

______       ______
x <= y   /\  y <= x    /\  z <= x     =>  z <= y

That is if x and y are not ordered, and z is below x, then it must also be
below y.

So in the Hasse diagrams below, the second order is layered but the first is not:

    a      c                     a    c
    |                            |   /
    |                            |  /
    |                            | /
    b                            b   

I hope my ascii art survives emailing :-)

I find it hard to believe that is not a standard definition, but have
not found it yet. Does anyone recognise this property?

TIA,

Adrian