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 * 1,j),(G * (len G),j)
let G be Go-board; :: thesis: ( 1 <= i & i <= len G & 1 <= j & j <= width G implies G * i,j in LSeg (G * 1,j),(G * (len G),j) )
assume that
A1: ( 1 <= i & i <= len G ) and
A2: ( 1 <= j & j <= width G ) ; :: thesis: G * i,j in LSeg (G * 1,j),(G * (len G),j)
A3: (G * i,j) `1 <= (G * (len G),j) `1 by A1, A2, SPRECT_3:25;
1 <= len G by A1, XXREAL_0:2;
then A4: (G * 1,j) `2 = (G * (len G),j) `2 by A2, GOBOARD5:2;
( (G * 1,j) `2 = (G * i,j) `2 & (G * 1,j) `1 <= (G * i,j) `1 ) by A1, A2, GOBOARD5:2, SPRECT_3:25;
hence G * i,j in LSeg (G * 1,j),(G * (len G),j) by A4, A3, GOBOARD7:9; :: thesis: verum