let G be Go-board; :: thesis: (G * (len G),(width G)) + |[1,1]| in Int (cell G,(len G),(width G))
set s1 = (G * (len G),(width G)) `2 ;
set r1 = (G * (len G),(width G)) `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 A2:
1 <= len G
by NAT_1:14;
then A3:
(G * (len G),1) `1 = (G * (len G),(width G)) `1
by A1, GOBOARD5:3;
A4:
(G * 1,(width G)) `2 = (G * (len G),(width G)) `2
by A1, A2, GOBOARD5:2;
G * (len G),(width G) = |[((G * (len G),(width G)) `1 ),((G * (len G),(width G)) `2 )]|
by EUCLID:57;
then A5:
(G * (len G),(width G)) + |[1,1]| = |[(((G * (len G),(width G)) `1 ) + 1),(((G * (len G),(width G)) `2 ) + 1)]|
by EUCLID:60;
A6:
((G * (len G),(width G)) `2 ) + 1 > (G * 1,(width G)) `2
by A4, XREAL_1:31;
A7:
((G * (len G),(width G)) `1 ) + 1 > (G * (len G),1) `1
by A3, XREAL_1:31;
Int (cell G,(len G),(width G)) = { |[r,s]| where r, s is Real : ( (G * (len G),1) `1 < r & (G * 1,(width G)) `2 < s ) }
by Th25;
hence
(G * (len G),(width G)) + |[1,1]| in Int (cell G,(len G),(width G))
by A5, A6, A7; :: thesis: verum