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,(j + 1)))) 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,(j + 1)))) 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,(j + 1)))) c= cell (G,i,j)
A5: LSeg ((G * (i,j)),(G * (i,(j + 1)))) c= v_strip (G,i) by A1, A2, A3, A4, Th14;
j + 1 <= width G by A4, NAT_1:13;
then LSeg ((G * (i,j)),(G * (i,(j + 1)))) c= h_strip (G,j) by A1, A2, A3, Th17;
hence LSeg ((G * (i,j)),(G * (i,(j + 1)))) c= cell (G,i,j) by A5, XBOOLE_1:19; :: thesis: verum