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