reserve n for Nat;

theorem Th1:
  for G be Go-board for i1,i2,j1,j2 be Nat st 1 <= j1 &
j1 <= width G & 1 <= j2 & j2 <= width G & 1 <= i1 & i1 < i2 & i2 <= len G holds
  G*(i1,j1)`1 < G*(i2,j2)`1
proof
  let G be Go-board;
  let i1,i2,j1,j2 be Nat;
  assume that
A1: 1 <= j1 and
A2: j1 <= width G and
A3: 1 <= j2 and
A4: j2 <= width G and
A5: 1 <= i1 and
A6: i1 < i2 and
A7: i2 <= len G;
A8: 1 <= i2 by A5,A6,XXREAL_0:2;
  then G*(i2,j1)`1 = G*(i2,1)`1 by A1,A2,A7,GOBOARD5:2
    .= G*(i2,j2)`1 by A3,A4,A7,A8,GOBOARD5:2;
  hence thesis by A1,A2,A5,A6,A7,GOBOARD5:3;
end;
