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Consequence

• Every element of a term algebra is denoted by one and only one constructor term

  f_i(T₁, ..., T_mi, S₁, ..., S_ni)

  for some terms T₁, ..., T_mi, S₁, ..., S_ni where the S₁, ..., S_ni are also constructor terms.
• One to one correspondence between terms and set elements.

We may define functions and predicates in term algebras inductively .