pushing all the initial subgoals

The value of this flag is normally nil. If you want to prevent the theorem prover from abandoning its initial work upon pushing the second subgoal, set :otf-flg to t.

Suppose you submit a conjecture to the theorem prover and the system splits it up into many subgoals. Any subgoal not proved by other methods is eventually set aside for an attempted induction proof. But upon setting aside the second such subgoal, the system chickens out and decides that rather than prove n>1 subgoals inductively, it will abandon its initial work and attempt induction on the originally submitted conjecture. The :otf-flg (Onward Thru the Fog) allows you to override this chickening out. When :otf-flg is t, the system will push all the initial subgoals and proceed to try to prove each, independently, by induction.

Even when you don't expect induction to be used or to succeed, setting the :otf-flg is a good way to force the system to generate and display all the initial subgoals.

For defthm and thm, :otf-flg is a keyword argument that is a peer to :rule-classes and :hints. It may be supplied as in the following examples; also see defthm.

(thm (my-predicate x y) :rule-classes nil :otf-flg t)

(defthm append-assoc (equal (append (append x y) z) (append x (append y z))) :hints (("Goal" :induct t)) :otf-flg t)

The :otf-flg may be supplied to defun via the xargs declare option. When you supply an :otf-flg hint to defun, the flag is effective for the termination proofs and the guard proofs, if any.