The interpretation of for example here involves abstracting the meaning of its matrix structure with respect to the material to its right, then making an assertion with respect to this abstraction.
if the LF contributed by the matrix clause of (42A) is, roughly, i. contain(box1,hematite1) then the LF resulting from the addition of for example can be written either with set notation (as in (ii)), taking an entity to exemplify a set, or with λ-notation (as in (iii)), taking an entity to exemplify a property: ii.