reserve f for non empty FinSequence of TOP-REAL 2,
  i,j,k,k1,k2,n,i1,i2,j1,j2 for Nat,
  r,s,r1,r2 for Real,
  p,q,p1,q1 for Point of TOP-REAL 2,
  G for Go-board;
reserve f for non constant standard special_circular_sequence;

theorem
  width GoB f > 1
proof
A1: width GoB f <> 0 by MATRIX_0:def 10;
  1 in dom f by FINSEQ_5:6;
  then consider i2,j2 such that
A2: [i2,j2] in Indices GoB f and
A3: f/.1 = (GoB f)*(i2,j2) by GOBOARD2:14;
A4: 1 <= j2 by A2,MATRIX_0:32;
  assume width GoB f <= 1;
  then
A5: width GoB f = 1 by A1,NAT_1:25;
  then j2 <= 1 by A2,MATRIX_0:32;
  then
A6: j2 = 1 by A4,XXREAL_0:1;
  consider i such that
A7: i in dom f and
A8: (f/.i)`2 <> (f/.1)`2 by Th31;
  consider i1,j1 such that
A9: [i1,j1] in Indices GoB f and
A10: f/.i = (GoB f)*(i1,j1) by A7,GOBOARD2:14;
A11: 1 <= i1 & i1 <= len GoB f by A9,MATRIX_0:32;
A12: 1 <= j1 by A9,MATRIX_0:32;
  j1 <= 1 by A5,A9,MATRIX_0:32;
  then j1 = 1 by A12,XXREAL_0:1;
  then
A13: (GoB f)*(i1,j1)`2 = (GoB f)*(1,1)`2 by A5,A11,GOBOARD5:1;
  1 <= i2 & i2 <= len GoB f by A2,MATRIX_0:32;
  hence contradiction by A5,A8,A10,A3,A13,A6,GOBOARD5:1;
end;
