Ltac splittablex_tac A :=
match A with
| _ <= _ < _ => fail 1
| _ < _ <= _ => fail 1
| _ <= _ <= _ => fail 1
| _ < _ < _ => fail 1
| _ <-> _ => fail 1
| _ /\ _ => apply Logic.I
end.
Definition splittablex (A: Prop) := True.

Lemma and_assoc_splittablex {T}{NT: NatDed T}: forall A B C: Prop,
splittablex (A /\ B) ->
!! ((A /\ B) /\ C) = !! (A /\ (B /\ C)).