reserve i,i1,i2,i9,i19,j,j1,j2,j9,j19,k,l,m,n for Nat;
reserve r,s,r9,s9 for Real;
reserve D for set,
  f for FinSequence of D,
  G for Matrix of D;
reserve G for Go-board,
  p for Point of TOP-REAL 2;

theorem
  for f being non empty FinSequence of TOP-REAL 2 st
  len f >= 2 & f is_sequence_on G holds f is non constant
proof
  let f be non empty FinSequence of TOP-REAL 2 such that
A1: len f >= 2 and
A2: f is_sequence_on G;
  assume
A3: for n,m st n in dom f & m in dom f holds f.n = f.m;
  1 <= len f by A1,XXREAL_0:2;
  then
A4: 1 in dom f by FINSEQ_3:25;
  then consider i1,j1 such that
A5: [i1,j1] in Indices G and
A6: f/.1 = G*(i1,j1) by A2;
A7: 1+1 in dom f by A1,FINSEQ_3:25;
  then consider i2,j2 such that
A8: [i2,j2] in Indices G and
A9: f/.2 = G*(i2,j2) by A2;
A10: f/.1 = f.1 by A4,PARTFUN1:def 6
    .= f.2 by A3,A4,A7
    .= f/.2 by A7,PARTFUN1:def 6;
  then
A11: i1 = i2 by A5,A6,A8,A9,GOBOARD1:5;
A12: j1 = j2 by A5,A6,A8,A9,A10,GOBOARD1:5;
A13: |.i1-i2.| = 0 by A11,ABSVALUE:2;
  |.i1-i2.| + |.j1-j2.| = 1 by A2,A4,A5,A6,A7,A8,A9;
  hence contradiction by A12,A13;
end;
