\DOC LIST_INDUCT_TAC \TYPE {LIST_INDUCT_TAC : tactic} \SYNOPSIS Performs tactical proof by structural induction on lists. \KEYWORDS tactic, list, induction. \DESCRIBE {LIST_INDUCT_TAC} reduces a goal {!l.P[l]}, where {l} ranges over lists, to two subgoals corresponding to the base and step cases in a proof by structural induction on {l}. The induction hypothesis appears among the assumptions of the subgoal for the step case. The specification of {LIST_INDUCT_TAC} is: { A ?- !l. P ===================================================== LIST_INDUCT_TAC A |- P[NIL/l] A u {{P[l'/l]}} ?- !h. P[CONS h l'/l] } where {l'} is a primed variant of {l} that does not appear free in the assumptions {A} (usually, {l'} is just {l}). When {LIST_INDUCT_TAC} is applied to a goal of the form {!l.P}, where {l} does not appear free in {P}, the subgoals are just {A ?- P} and {A u {{P}} ?- !h.P}. \FAILURE {LIST_INDUCT_TAC g} fails unless the conclusion of the goal {g} has the form {!l.t}, where the variable {l} has type {(ty)list} for some type {ty}. \SEEALSO EQ_LENGTH_INDUCT_TAC, EQ_LENGTH_SNOC_INDUCT_TAC, LIST_INDUCT, SNOC_INDUCT_TAC. \ENDDOC