Fact eq_rect_combine_dist_helper1 : forall a b c d, b * c = d -> (a + b) * c = a * c + d.Fact eq_rect_combine_dist_helper2 : forall a b c d, b * c = d -> a * c + d = (a + b) * c.

Theorem combine_inj : forall sz1 sz2 a b c d, @combine sz1 a sz2 b = @combine sz1 c sz2 d -> a = c /\ b = d.