Truth lemma for a Henkin term model
= Truth lemma for a Henkin term model
A sentence with closed-term parameters holds in a <term model> if and only if it belongs to the complete consistent theory defining that model. Prove this by <structural induction>: atoms are the definition, Boolean steps use completeness and consistency, and existential sentences use the <Henkin witness property>. Conversely any existential witness represented by a term gives the existential sentence by logical inference.