let i, j be Element of 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_3:24;
1 <= width G by A2, XXREAL_0:2;
then A4: (G * i,1) `1 = (G * i,(width G)) `1 by A1, GOBOARD5:3;
( (G * i,1) `1 = (G * i,j) `1 & (G * i,1) `2 <= (G * i,j) `2 ) by A1, A2, GOBOARD5:3, SPRECT_3:24;
hence G * i,j in LSeg (G * i,1),(G * i,(width G)) by A4, A3, GOBOARD7:8; :: thesis: verum