BOOL_CASES_TAC : (term -> tactic)
Performs boolean case analysis on a (free) term in the goal.
When applied to a term x (which must be of type bool but need not be simply a variable), and a goal A ?- t, the tactic BOOL_CASES_TAC generates the two subgoals corresponding to A ?- t but with any free instances of x replaced by F and T respectively.
              A ?- t
   ============================  BOOL_CASES_TAC "x"
    A ?- t[F/x]    A ?- t[T/x]
The term given does not have to be free in the goal, but if it isn’t, BOOL_CASES_TAC will merely duplicate the original goal twice.
Fails unless the term x has type bool.
The goal:
   ?- (b ==> ~b) ==> (b ==> a)
can be completely solved by using BOOL_CASES_TAC on the variable b, then simply rewriting the two subgoals using only the inbuilt tautologies, i.e. by applying the following tactic:
   BOOL_CASES_TAC (Parse.Term `b:bool`) THEN REWRITE_TAC[]

Avoiding fiddly logical proofs by brute-force case analysis, possibly only over a key term as in the above example, possibly over all free boolean variables.
HOL  Kananaskis-14