let f be non constant standard special_circular_sequence; :: thesis: LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|)) misses L~ f
A1: 1 <= len (GoB f) by GOBOARD7:32;

now :: thesis: for p being Point of (TOP-REAL 2) st p in LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|)) holds
p `1 < ((GoB f) * (1,1)) `1

1 < width (GoB f) by GOBOARD7:33;
then 1 + 1 <= width (GoB f) by NAT_1:13;
then A2: ((GoB f) * (1,2)) `1 = ((GoB f) * (1,1)) `1 by A1, GOBOARD5:2;
(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|) `1 = (((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) `1) - (|[1,0]| `1) by TOPREAL3:3
.= ((1 / 2) * ((((GoB f) * (1,1)) + ((GoB f) * (1,2))) `1)) - (|[1,0]| `1) by TOPREAL3:4
.= ((1 / 2) * ((((GoB f) * (1,1)) `1) + (((GoB f) * (1,1)) `1))) - (|[1,0]| `1) by A2, TOPREAL3:2
.= (1 * (((GoB f) * (1,1)) `1)) - 1 by EUCLID:52 ;
then A3: ((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]| = |[((((GoB f) * (1,1)) `1) - 1),((((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|) `2)]| by EUCLID:53;
(((GoB f) * (1,1)) - |[1,1]|) `1 = (((GoB f) * (1,1)) `1) - (|[1,1]| `1) by TOPREAL3:3
.= (((GoB f) * (1,1)) `1) - 1 by EUCLID:52 ;
then A4: ((GoB f) * (1,1)) - |[1,1]| = |[((((GoB f) * (1,1)) `1) - 1),((((GoB f) * (1,1)) - |[1,1]|) `2)]| by EUCLID:53;
let p be Point of (TOP-REAL 2); :: thesis: ( p in LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|)) implies p `1 < ((GoB f) * (1,1)) `1 )
assume p in LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|)) ; :: thesis: p `1 < ((GoB f) * (1,1)) `1
then p `1 = (((GoB f) * (1,1)) `1) - 1 by A4, A3, TOPREAL3:11;
hence p `1 < ((GoB f) * (1,1)) `1 by XREAL_1:44; :: thesis: verum

end;

hence LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (1,2)))) - |[1,0]|)) misses L~ f by Th21; :: thesis: verum