set AR = L -waybelow ;
let x, y, z, u be Element of L; WAYBEL_4:def 4 ( u <= x & [x,y] in L -waybelow & y <= z implies [u,z] in L -waybelow )
assume that
A1:
u <= x
and
A2:
[x,y] in L -waybelow
and
A3:
y <= z
; [u,z] in L -waybelow
x << y
by A2, Def1;
then
u << z
by A1, A3, WAYBEL_3:2;
hence
[u,z] in L -waybelow
by Def1; verum