... f (a1 , . . . , an ), where each aj ∈ Xi . So aj ∈ hXi by hypothesis. Since hXi is
inductive, f (a1 , . . . , an ) ∈ hXi, and hence a ∈ hXi as well. This shows that
Xi+1 ⊆ A, and consequently X ⊆ hXi.
The inductive set A is said to be freely generated by X (with respect to F ),
if the following con ...