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Generalized Induction Principle

We want to prove

forall x in S: F.

Idea: exery element x in S is denoted by some term

f_i(x₁,...,x_mi, y₁, ..., y_ni).

Let the induction run over the structure of every such term:

• assume that F holds for every "S-component" y_j of x, and
• show that F is propagated to x itself.