CHECK_ASSUME_TAC : thm_tactic
Adds a theorem to the assumption list of goal, unless it solves the goal.
When applied to a theorem A' |- s and a goal A ?- t, the tactic CHECK_ASSUME_TAC checks whether the theorem will solve the goal (this includes the possibility that the theorem is just A' |- F). If so, the goal is duly solved. If not, the theorem is added to the assumptions of the goal, unless it is already there.
       A ?- t
   ==============  CHECK_ASSUME_TAC (A' |- F)   [special case 1]

       A ?- t
   ==============  CHECK_ASSUME_TAC (A' |- t)   [special case 2]

       A ?- t
   ==============  CHECK_ASSUME_TAC (A' |- s)   [general case]
    A u {s} ?- t
Unless A' is a subset of A, the tactic will be invalid, although it will not fail.
Never fails.
HOL  Kananaskis-14