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
  1 <= i & i <= len G & 1 <= j & j <= width G implies G*(i,j) in LSeg(G*
  (i,1),G*(i,width G))
proof
  assume that
A1: 1 <= i & i <= len G and
A2: 1 <= j & j <= width G;
A3: G*(i,j)`2 <= G* (i,width G)`2 by A1,A2,SPRECT_3:12;
  1 <= width G by A2,XXREAL_0:2;
  then
A4: G*(i,1)`1 = G* (i,width G)`1 by A1,GOBOARD5:2;
  G*(i,1)`1 = G*(i,j)`1 & G*(i,1)`2 <= G*(i,j)`2 by A1,A2,GOBOARD5:2
,SPRECT_3:12;
  hence thesis by A4,A3,GOBOARD7:7;
end;
