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 * (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_3:13;
1 <= len G by A1, XXREAL_0:2;
then A4: (G * (1,j)) `2 = (G * ((len G),j)) `2 by A2, GOBOARD5:1;
( (G * (1,j)) `2 = (G * (i,j)) `2 & (G * (1,j)) `1 <= (G * (i,j)) `1 ) by A1, A2, GOBOARD5:1, SPRECT_3:13;
hence G * (i,j) in LSeg ((G * (1,j)),(G * ((len G),j))) by A4, A3, GOBOARD7:8; :: thesis: verum