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) * (2,1)))) - |[0,1]|)) misses L~ f
A1: 1 <= width (GoB f) by GOBOARD7:33;

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) * (2,1)))) - |[0,1]|)) holds
p `2 < ((GoB f) * (1,1)) `2

1 < len (GoB f) by GOBOARD7:32;
then 1 + 1 <= len (GoB f) by NAT_1:13;
then A2: ((GoB f) * (2,1)) `2 = ((GoB f) * (1,1)) `2 by A1, GOBOARD5:1;
(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) - |[0,1]|) `2 = (((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) `2) - (|[0,1]| `2) by TOPREAL3:3
.= ((1 / 2) * ((((GoB f) * (1,1)) + ((GoB f) * (2,1))) `2)) - (|[0,1]| `2) by TOPREAL3:4
.= ((1 / 2) * ((((GoB f) * (1,1)) `2) + (((GoB f) * (1,1)) `2))) - (|[0,1]| `2) by A2, TOPREAL3:2
.= (1 * (((GoB f) * (1,1)) `2)) - 1 by EUCLID:52 ;
then A3: ((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) - |[0,1]| = |[((((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) - |[0,1]|) `1),((((GoB f) * (1,1)) `2) - 1)]| by EUCLID:53;
(((GoB f) * (1,1)) - |[1,1]|) `2 = (((GoB f) * (1,1)) `2) - (|[1,1]| `2) by TOPREAL3:3
.= (((GoB f) * (1,1)) `2) - 1 by EUCLID:52 ;
then A4: ((GoB f) * (1,1)) - |[1,1]| = |[((((GoB f) * (1,1)) - |[1,1]|) `1),((((GoB f) * (1,1)) `2) - 1)]| 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) * (2,1)))) - |[0,1]|)) implies p `2 < ((GoB f) * (1,1)) `2 )
assume p in LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) - |[0,1]|)) ; :: thesis: p `2 < ((GoB f) * (1,1)) `2
then p `2 = (((GoB f) * (1,1)) `2) - 1 by A4, A3, TOPREAL3:12;
hence p `2 < ((GoB f) * (1,1)) `2 by XREAL_1:44; :: thesis: verum

end;

hence LSeg ((((GoB f) * (1,1)) - |[1,1]|),(((1 / 2) * (((GoB f) * (1,1)) + ((GoB f) * (2,1)))) - |[0,1]|)) misses L~ f by Th23; :: thesis: verum