(primitive) split into two cases

(casesplit (< x y)) -- assuming that we are at the top of the
                       conclusion, add (< x y) as a new top-level
                       hypothesis in the current goal, and create a
                       subgoal identical to the current goal except
                       that it has (not (< x y)) as a new top-level

General Form: (casesplit expr &optional use-hyps-flag do-not-flatten-flag)

When the current subterm is the entire conclusion, this instruction adds expr as a new top-level hypothesis, and create a subgoal identical to the existing current goal except that it has the negation of expr as a new top-level hypothesis. See also claim. The optional arguments control the use of governors and the ``flattening'' of new hypotheses, as we now explain.

The argument use-hyps-flag is only of interest when there are governors. (To read about governors, see the documentation for the command hyps). In that case, if use-hyps-flag is not supplied or is nil, then the description above is correct; but otherwise, it is not expr but rather it is (implies govs expr) that is added as a new top-level hypothesis (and whose negation is added as a top-level hypothesis for the new goal), where govs is the conjunction of the governors.

If do-not-flatten-flag is supplied and not nil, then that is all there is to this command. Otherwise (thus this is the default), when the claimed term (first argument) is a conjunction (and) of terms and the claim instruction succeeds, then each (nested) conjunct of the claimed term is added as a separate new top-level hypothesis. Consider the following example, assuming there are no governors.

(casesplit (and (and (< x y) (integerp a)) (equal r s)) t)
Three new top-level hypotheses are added to the current goal, namely (< x y), (integerp a), and (equal r s). In that case, only one hypothesis is added to create the new goal, namely the negation of (and (< x y) (integerp a) (equal r s)). If the negation of this term had been claimed, then it would be the other way around: the current goal would get a single new hypothesis while the new goal would be created by adding three hypotheses.

Note: It is allowed to use abbreviations in the hints.