Condition 1 is required because one could only reliably deduce an untyped proband carry a haplotype if a descendant inherited it. Conditions 2 and 3 ensure that the chance that the shared haplotype was transmitted to the descendant through the mate instead of the proband is small. If the descendant is a grandchild, in addition to the mate of the proband, data are needed to show that the sharing of the haplotype did not go through the other two grandparents instead.
