reserve i,j,k,i1,j1 for Nat,
  p for Point of TOP-REAL 2,
  x for set;
reserve f for non constant standard special_circular_sequence;
reserve P for Subset of TOP-REAL 2;

theorem
  LSeg((GoB f)*(1,width GoB f)+|[-1,1]|, 1/2*((GoB f)*(1,width GoB f)+(
  GoB f)*(2,width GoB f))+|[0,1]|) misses L~f
proof
A1: 1 <= width GoB f by GOBOARD7:33;
  now
    1 < len GoB f by GOBOARD7:32;
    then 1+1 <= len GoB f by NAT_1:13;
    then
A2: (GoB f)*(2,width GoB f)`2 = (GoB f)*(1,width GoB f)`2 by A1,GOBOARD5:1;
    (1/2*((GoB f)*(1,width GoB f)+(GoB f)*(2,width GoB f))+|[0,1]|)`2 = (1
/2*((GoB f)*(1,width GoB f)+(GoB f)*(2,width GoB f)))`2+|[0,1]|`2 by TOPREAL3:2
      .= 1/2*((GoB f)*(1,width GoB f)+(GoB f)*(2,width GoB f))`2+|[0,1]|`2
    by TOPREAL3:4
      .= 1/2*((GoB f)*(1,width GoB f)`2+(GoB f)*(1,width GoB f)`2)+|[0,1]|`2
    by A2,TOPREAL3:2
      .= 1*((GoB f)*(1,width GoB f))`2+1 by EUCLID:52;
    then
A3: 1/2*((GoB f)*(1,width GoB f)+(GoB f)*(2,width GoB f))+|[0,1]| = |[(1/
    2*((GoB f)*(1,width GoB f)+(GoB f)*(2,width GoB f))+|[0,1]|)`1, (GoB f)*(1,
    width GoB f)`2+1]| by EUCLID:53;
    ((GoB f)*(1,width GoB f)+|[-1,1]|)`2 = ((GoB f)*(1,width GoB f))`2+|[-
    1,1]|`2 by TOPREAL3:2
      .= (GoB f)*(1,width GoB f)`2+1 by EUCLID:52;
    then
A4: (GoB f)*(1,width GoB f)+|[-1,1]| = |[((GoB f)*(1,width GoB f)+|[-1,1]|
    )`1,(GoB f)*(1,width GoB f)`2+1]| by EUCLID:53;
    let p;
    assume p in LSeg((GoB f)*(1,width GoB f)+|[-1,1]|, 1/2*((GoB f)*(1,width
    GoB f)+(GoB f)*(2,width GoB f))+|[0,1]|);
    then p`2 = (GoB f)*(1,width GoB f)`2 + 1 by A4,A3,TOPREAL3:12;
    hence p`2 > (GoB f)*(1,width GoB f)`2 by XREAL_1:29;
  end;
  hence thesis by Th24;
end;
