let i, j be Nat; 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; ( 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
; 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; verum