LIST_INDUCT : ((thm # thm) -> thm)
A1 |- P[NIL/l] A2 |- !t. P[t/l] ==> !h. P[CONS h t/l] ------------------------------------------------------------ LIST_INDUCT A1 u A2 |- !l. PWhen supplied with a theorem A1 |- P[NIL], which asserts the base case of a proof of the proposition P[l] by structural induction on the list l, and the theorem
A2 |- !t. P[t] ==> !h. P[CONS h t]which asserts the step case in the induction on l, the inference rule LIST_INDUCT returns A1 u A2 |- !l. P[l].