let G be Go-board; :: thesis: (G * (len G),1) + |[1,(- 1)]| in Int (cell G,(len G),0 )
set s1 = (G * (len G),1) `2 ;
set r1 = (G * (len G),1) `1 ;
width G <> 0
by GOBOARD1:def 5;
then A1:
1 <= width G
by NAT_1:14;
len G <> 0
by GOBOARD1:def 5;
then
1 <= len G
by NAT_1:14;
then A2:
(G * 1,1) `2 = (G * (len G),1) `2
by A1, GOBOARD5:2;
G * (len G),1 = |[((G * (len G),1) `1 ),((G * (len G),1) `2 )]|
by EUCLID:57;
then A3: (G * (len G),1) + |[1,(- 1)]| =
|[(((G * (len G),1) `1 ) + 1),(((G * (len G),1) `2 ) + (- 1))]|
by EUCLID:60
.=
|[(((G * (len G),1) `1 ) + 1),(((G * (len G),1) `2 ) - 1)]|
;
(G * (len G),1) `2 < ((G * 1,1) `2 ) + 1
by A2, XREAL_1:31;
then A4:
((G * (len G),1) `2 ) - 1 < (G * 1,1) `2
by XREAL_1:21;
A5:
((G * (len G),1) `1 ) + 1 > (G * (len G),1) `1
by XREAL_1:31;
Int (cell G,(len G),0 ) = { |[r,s]| where r, s is Real : ( (G * (len G),1) `1 < r & s < (G * 1,1) `2 ) }
by Th24;
hence
(G * (len G),1) + |[1,(- 1)]| in Int (cell G,(len G),0 )
by A3, A4, A5; :: thesis: verum