reserve n for Nat,
  i,j for Nat,
  r,s,r1,s1,r2,s2,r9,s9 for Real,
  p,q for Point of TOP-REAL 2,
  G for Go-board,
  x,y for set,
  v for Point of Euclid 2;

theorem Th38:
  G*(1,width G)+|[-1,1]| in Int cell(G,0,width G)
proof
  set s1 = G*(1,width G)`2, r1 = G*(1,width G)`1;
  len G <> 0 by MATRIX_0:def 10;
  then
A1: 1 <= len G by NAT_1:14;
  width G <> 0 by MATRIX_0:def 10;
  then 1 <= width G by NAT_1:14;
  then G*(1,1)`1 = r1 by A1,GOBOARD5:2;
  then r1 < G*(1,1)`1+1 by XREAL_1:29;
  then
A2: s1+1 > G*(1,width G)`2 & r1-1 < G*(1,1)`1 by XREAL_1:19,29;
  G*(1,width G) = |[r1,s1]| by EUCLID:53;
  then
A3: G*(1,width G)+|[-1,1]| = |[r1+-1,s1+1]| by EUCLID:56
    .= |[r1-1,s1+1]|;
  Int cell(G,0,width G) = { |[r,s]| : r < G*(1,1)`1 & G*(1,width G)`2 < s
  } by Th19;
  hence thesis by A3,A2;
end;
