theorem
  width G = m+1 & m>0 & k in Seg m & n in dom G implies k in Seg
  width G & DelCol(G,width G)*(n,k) = G*(n,k) & width G in Seg width G
proof
  assume that
A1: width G = m+1 and
A2: m>0 and
A3: k in Seg m and
A4: n in dom G;
  k<=m by A3,FINSEQ_1:1;
  then
A5: k<width G by A1,NAT_1:13;
  1<=width G by A1,A2,SEQM_3:43;
  then
A6: width G in Seg width G by FINSEQ_1:1;
  1<=k by A3,FINSEQ_1:1;
  hence thesis by A1,A2,A4,A6,A5,Th69;
end;
