theorem
  max(i,j,m,n) = i or max(i,j,m,n) = j or max(i,j,m,n) = m or max(i,j,m, n) = n
proof
A1: max(m,n) = m or max(m,n) = n by XXREAL_0:16;
  max(i,j) = i or max(i,j) = j by XXREAL_0:16;
  hence thesis by A1,XXREAL_0:16;
end;
