let i, j be 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, Th16;
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, Th20;
hence LSeg ((G * (i,j)),(G * ((i + 1),j))) c= cell (G,i,j) by A5, XBOOLE_1:19; :: thesis: verum