split into two cases
Major Section: PROOF-CHECKER-COMMANDS
Example:
(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
hypothesis
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.
Remark: It is allowed to use abbreviations in the hints.