let i, j be Nat; :: thesis: for G being Go-board st 1 <= i & i <= len G & 1 <= j & j <= width G holds
G * (i,j) in LSeg ((G * (i,1)),(G * (i,(width G))))
let G be Go-board; :: thesis: ( 1 <= i & i <= len G & 1 <= j & j <= width G implies G * (i,j) in LSeg ((G * (i,1)),(G * (i,(width G)))) )
assume that
A1: ( 1 <= i & i <= len G ) and
A2: ( 1 <= j & j <= width G ) ; :: thesis: G * (i,j) in LSeg ((G * (i,1)),(G * (i,(width G))))
A3: (G * (i,j)) `2 <= (G * (i,(width G))) `2 by A1, A2, SPRECT_3:12;
1 <= width G by A2, XXREAL_0:2;
then A4: (G * (i,1)) `1 = (G * (i,(width G))) `1 by A1, GOBOARD5:2;
( (G * (i,1)) `1 = (G * (i,j)) `1 & (G * (i,1)) `2 <= (G * (i,j)) `2 ) by A1, A2, GOBOARD5:2, SPRECT_3:12;
hence G * (i,j) in LSeg ((G * (i,1)),(G * (i,(width G)))) by A4, A3, GOBOARD7:7; :: thesis: verum