theorem
  min(i,j,m,n) = i or min(i,j,m,n) = j or min(i,j,m,n) = m or min(i,j,m, n) = n
proof
A1: min(m,n) = m or min(m,n) = n by XXREAL_0:15;
  min(i,j) = i or min(i,j) = j by XXREAL_0:15;
  hence thesis by A1,XXREAL_0:15;
end;
