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
LSeg (G * i,j),(G * (i + 1),j) c= cell G,i,j
let G be Go-board; :: thesis: ( 1 <= i & i < len G & 1 <= j & j <= width G implies LSeg (G * i,j),(G * (i + 1),j) c= cell G,i,j )
assume that
A1: 1 <= i and
A2: i < len G and
A3: 1 <= j and
A4: j <= width G ; :: thesis: LSeg (G * i,j),(G * (i + 1),j) c= cell G,i,j
A5: LSeg (G * i,j),(G * (i + 1),j) c= h_strip G,j by A1, A2, A3, A4, Th17;
i + 1 <= len G by A2, NAT_1:13;
then LSeg (G * i,j),(G * (i + 1),j) c= v_strip G,i by A1, A3, A4, Th21;
hence LSeg (G * i,j),(G * (i + 1),j) c= cell G,i,j by A5, XBOOLE_1:19; :: thesis: verum