SNOC_INDUCT_TAC

listLib.SNOC_INDUCT_TAC : tactic

Performs tactical proof by structural induction on lists.

SNOC_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 from the tail end. The induction hypothesis appears among the assumptions of the subgoal for the step case. The specification of SNOC_INDUCT_TAC is:

                     A ?- !l. P
   =====================================================  SNOC_INDUCT_TAC
    A |- P[NIL/l]   A u {{P[l'/l]}} ?- !x. P[SNOC x 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 SNOC_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

SNOC_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.

See also

listLib.EQ_LENGTH_INDUCT_TAC, listLib.EQ_LENGTH_SNOC_INDUCT_TAC, listLib.LIST_INDUCT_TAC