let m, k, n be Element of NAT ; :: thesis: for G being Go-board st width G = m + 1 & m > 0 & k in Seg m & n in dom G holds
( (DelCol G,1) * n,k = G * n,(k + 1) & 1 in Seg (width G) )
let G be Go-board; :: thesis: ( width G = m + 1 & m > 0 & k in Seg m & n in dom G implies ( (DelCol G,1) * n,k = G * n,(k + 1) & 1 in Seg (width G) ) )
assume A1: ( width G = m + 1 & m > 0 & k in Seg m & n in dom G ) ; :: thesis: ( (DelCol G,1) * n,k = G * n,(k + 1) & 1 in Seg (width G) )
then 1 <= width G by Th3;
then ( 1 in Seg (width G) & 1 <= k & k <= m ) by A1, FINSEQ_1:3;
hence ( (DelCol G,1) * n,k = G * n,(k + 1) & 1 in Seg (width G) ) by A1, Th32; :: thesis: verum