reserve i, i1, i2, j, j1, j2, k, m, n, t for Nat,
  D for non empty Subset of TOP-REAL 2,
  E for compact non vertical non horizontal Subset of TOP-REAL 2,
  C for compact connected non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p, q, x for Point of TOP-REAL 2,
  r, s for Real;

theorem Th18:
  1 <= j1 & j1 <= width G & 1 <= j2 & j2 <= width G & 1 <= i1 & i1
  <= i2 & i2 <= len G implies G*(i1,j1)`1 <= G*(i2,j2)`1
proof
  assume that
A1: 1 <= j1 & j1 <= width G and
A2: 1 <= j2 & j2 <= width G and
A3: 1 <= i1 & i1 <= i2 and
A4: i2 <= len G;
A5: 1 <= i2 by A3,XXREAL_0:2;
  then G*(i2,j1)`1 = G*(i2,1)`1 by A1,A4,GOBOARD5:2
    .= G*(i2,j2)`1 by A2,A4,A5,GOBOARD5:2;
  hence thesis by A1,A3,A4,SPRECT_3:13;
end;
