theorem Th59:
  1 <= k & k <= len Cage(C,n) & 1 <= t & t <= width (Gauge(C,n)) &
  Cage(C,n)/.k = Gauge(C,n)*(1,t) implies Cage(C,n)/.k in W-most L~Cage(C,n)
proof
  assume that
A1: 1 <= k & k <= len Cage(C,n) and
A2: 1 <= t & t <= width (Gauge(C,n)) and
A3: Cage(C,n)/.k = Gauge(C,n)*(1,t);
  Cage(C,n) is_sequence_on Gauge(C,n) by JORDAN9:def 1;
  then
A4: (Gauge(C,n)*(1,t))`1 <= W-bound L~Cage(C,n) by A2,Th21;
  len Cage(C,n) >= 2 by GOBOARD7:34,XXREAL_0:2;
  then
A5: Cage(C,n)/.k in L~Cage(C,n) by A1,TOPREAL3:39;
  then W-bound L~Cage(C,n) <= (Cage(C,n)/.k)`1 by PSCOMP_1:24;
  hence thesis by A3,A5,A4,SPRECT_2:12,XXREAL_0:1;
end;
