let f be non constant standard special_circular_sequence; :: thesis: LSeg (((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]|),(((GoB f) * 1,(width (GoB f))) + |[(- 1),1]|) misses L~ f
A1: 1 <= len (GoB f) by GOBOARD7:34;

now

A2: 1 < width (GoB f) by GOBOARD7:35;
then A3: ((width (GoB f)) -' 1) + 1 = width (GoB f) by XREAL_1:237;
then A4: (width (GoB f)) -' 1 <= width (GoB f) by NAT_1:11;
A5: ((GoB f) * 1,(width (GoB f))) `1 = ((GoB f) * 1,1) `1 by A1, A2, GOBOARD5:3;
then (((GoB f) * 1,(width (GoB f))) + |[(- 1),1]|) `1 = (((GoB f) * 1,1) `1 ) + (|[(- 1),1]| `1 ) by TOPREAL3:7
.= (((GoB f) * 1,1) `1 ) + (- 1) by EUCLID:56
.= (((GoB f) * 1,1) `1 ) - 1 ;
then A6: ((GoB f) * 1,(width (GoB f))) + |[(- 1),1]| = |[((((GoB f) * 1,1) `1 ) - 1),((((GoB f) * 1,(width (GoB f))) + |[(- 1),1]|) `2 )]| by EUCLID:57;
1 <= (width (GoB f)) -' 1 by A2, A3, NAT_1:13;
then A7: ((GoB f) * 1,((width (GoB f)) -' 1)) `1 = ((GoB f) * 1,1) `1 by A1, A4, GOBOARD5:3;
(((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]|) `1 = (((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) `1 ) - (|[1,0 ]| `1 ) by TOPREAL3:8
.= ((1 / 2) * ((((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f)))) `1 )) - (|[1,0 ]| `1 ) by TOPREAL3:9
.= ((1 / 2) * ((((GoB f) * 1,1) `1 ) + (((GoB f) * 1,1) `1 ))) - (|[1,0 ]| `1 ) by A7, A5, TOPREAL3:7
.= (1 * (((GoB f) * 1,1) `1 )) - 1 by EUCLID:56 ;
then A8: ((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]| = |[((((GoB f) * 1,1) `1 ) - 1),((((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]|) `2 )]| by EUCLID:57;
let p be Point of (TOP-REAL 2); :: thesis: ( p in LSeg (((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]|),(((GoB f) * 1,(width (GoB f))) + |[(- 1),1]|) implies p `1 < ((GoB f) * 1,1) `1 )
assume p in LSeg (((1 / 2) * (((GoB f) * 1,((width (GoB f)) -' 1)) + ((GoB f) * 1,(width (GoB f))))) - |[1,0 ]|),(((GoB f) * 1,(width (GoB f))) + |[(- 1),1]|) ; :: thesis: p `1 < ((GoB f) * 1,1) `1
then p `1 = (((GoB f) * 1,1) `1 ) - 1 by A8, A6, TOPREAL3:17;
hence p `1 < ((GoB f) * 1,1) `1 by XREAL_1:46; :: thesis: verum

end;

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