reserve n for Nat;

theorem Th2:
  for G be Go-board for i1,i2,j1,j2 be Nat st 1 <= i1 &
i1 <= len G & 1 <= i2 & i2 <= len G & 1 <= j1 & j1 < j2 & j2 <= width G holds G
  *(i1,j1)`2 < G*(i2,j2)`2
proof
  let G be Go-board;
  let i1,i2,j1,j2 be Nat;
  assume that
A1: 1 <= i1 and
A2: i1 <= len G and
A3: 1 <= i2 and
A4: i2 <= len G and
A5: 1 <= j1 and
A6: j1 < j2 and
A7: j2 <= width G;
A8: 1 <= j2 by A5,A6,XXREAL_0:2;
  then G*(i1,j2)`2 = G*(1,j2)`2 by A1,A2,A7,GOBOARD5:1
    .= G*(i2,j2)`2 by A3,A4,A7,A8,GOBOARD5:1;
  hence thesis by A1,A2,A5,A6,A7,GOBOARD5:4;
end;
