theorem Th63:
  i in Seg width G & width G = m+1 implies width DelCol(G,i) = m
proof
  set D = DelCol(G,i);
  assume that
A1: i in Seg width G and
A2: width G = m+1;
  width G <> 0 by A2;
  then 0<len G by Def3;
  then 0+1<=len G by NAT_1:13;
  then
 1 in dom G by FINSEQ_3:25;
  then
A3: Line(D,1) = Del(Line(G,1),i) by Th62;
A4: dom Line(G,1) = Seg len Line(G,1) & len Line(D,1) = width D by Def7,
FINSEQ_1:def 3;
  len Line(G,1) = m+1 by A2,Def7;
  hence thesis by A1,A2,A3,A4,FINSEQ_3:109;
end;
