let E be compact non horizontal non vertical Subset of (TOP-REAL 2); :: thesis: not cell ((Gauge (E,0)),2,2) c= BDD E
assume A1: cell ((Gauge (E,0)),2,2) c= BDD E ; :: thesis: contradiction
E c= cell ((Gauge (E,0)),2,2) by Th17;
then A2: E c= BDD E by A1;
set e = the Element of E;
A3: BDD E misses E by JORDAN1A:7;
the Element of E in E ;
hence contradiction by A2, A3, XBOOLE_0:3; :: thesis: verum