let j, i be Element of NAT ; :: thesis: for G being Go-board st j < width G & 1 <= i & i < len G holds
LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= cell G,i,j
let G be Go-board; :: thesis: ( j < width G & 1 <= i & i < len G implies LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= cell G,i,j )
assume that
A1: j < width G and
A2: 1 <= i and
A3: i < len G ; :: thesis: LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= cell G,i,j
A4: LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= h_strip G,j by A1, A2, A3, Th16;
A5: 1 <= j + 1 by NAT_1:11;
A6: i + 1 <= len G by A3, NAT_1:13;
j + 1 <= width G by A1, NAT_1:13;
then LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= v_strip G,i by A2, A5, A6, Th21;
hence LSeg (G * i,(j + 1)),(G * (i + 1),(j + 1)) c= cell G,i,j by A4, XBOOLE_1:19; :: thesis: verum