let E be compact non horizontal non vertical Subset of (TOP-REAL 2); not cell (Gauge E,0 ),2,2 c= BDD E
assume A1:
cell (Gauge E,0 ),2,2 c= BDD E
; contradiction
E c= cell (Gauge E,0 ),2,2
by Th18;
then A2:
E c= BDD E
by A1, XBOOLE_1:1;
consider e being Element of E;
A3:
BDD E misses E
by JORDAN1A:15;
e in E
;
hence
contradiction
by A2, A3, XBOOLE_0:3; verum