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 Th39:
  G*(len G,1)+|[1,-1]| in Int cell(G,len G,0)
proof
  set s1 = G*(len G,1)`2, r1 = G*(len G,1)`1;
A1: r1+1 > G*(len G,1)`1 by XREAL_1:29;
  len G <> 0 by MATRIX_0:def 10;
  then
A2: 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)`2 = s1 by A2,GOBOARD5:1;
  then s1 < G*(1,1)`2+1 by XREAL_1:29;
  then
A3: s1-1 < G*(1,1)`2 by XREAL_1:19;
  G*(len G,1) = |[r1,s1]| by EUCLID:53;
  then
A4: G*(len G,1)+|[1,-1]| = |[r1+1,s1+-1]| by EUCLID:56
    .= |[r1+1,s1-1]|;
  Int cell(G,len G,0) = { |[r,s]| : G*(len G,1)`1 < r & s < G* (1,1)`2 }
  by Th21;
  hence thesis by A4,A3,A1;
end;
