let i, j be Nat; :: thesis: for G being Go-board st i < len G & 1 <= j & j < width G holds
LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= cell (G,i,j)
let G be Go-board; :: thesis: ( i < len G & 1 <= j & j < width G implies LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= cell (G,i,j) )
assume that
A1: i < len G and
A2: 1 <= j and
A3: j < width G ; :: thesis: LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= cell (G,i,j)
A4: LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= v_strip (G,i) by A1, A2, A3, Th13;
A5: 1 <= i + 1 by NAT_1:11;
A6: i + 1 <= len G by A1, NAT_1:13;
j + 1 <= width G by A3, NAT_1:13;
then LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= h_strip (G,j) by A2, A5, A6, Th17;
hence LSeg ((G * ((i + 1),j)),(G * ((i + 1),(j + 1)))) c= cell (G,i,j) by A4, XBOOLE_1:19; :: thesis: verum