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 Th37:
  G*(len G,width G)+|[1,1]| in Int cell(G,len G,width G)
proof
  set s1 = G*(len G,width G)`2, r1 = G*(len G,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
A2: 1 <= width G by NAT_1:14;
  then G*(len G,1)`1 = r1 by A1,GOBOARD5:2;
  then
A3: r1+1 > G*(len G,1)`1 by XREAL_1:29;
  G*(len G,width G) = |[r1,s1]| by EUCLID:53;
  then
A4: G*(len G,width G)+|[1,1]| = |[r1+1,s1+1]| by EUCLID:56;
  G*(1,width G)`2 = s1 by A2,A1,GOBOARD5:1;
  then
A5: s1+1 > G*(1,width G)`2 by XREAL_1:29;
  Int cell(G,len G,width G) = { |[r,s]| : G*(len G,1)`1 < r & G*(1,width
  G)`2 < s } by Th22;
  hence thesis by A4,A5,A3;
end;
