reserve p,q for Point of TOP-REAL 2,
  i,i1,i2,j,j1,j2,k for Nat,
  r,s for Real,
  G for Matrix of TOP-REAL 2;

theorem Th12:
  for f being standard non empty FinSequence of TOP-REAL 2,
  n being Nat st n in dom f & n+1 in dom f
  for m,k,i,j being Nat
  st [m,k] in Indices GoB f & [i,j] in Indices GoB f &
  f/.n = (GoB f)*(m,k) & f/.(n+1) = (GoB f)*(i,j) holds |.m-i.|+|.k-j.| = 1
proof
  let f be standard non empty FinSequence of TOP-REAL 2, n be Nat such that
A1: n in dom f and
A2: n+1 in dom f;
  f is_sequence_on GoB f by Def5;
  hence thesis by A1,A2;
end;
