EXISTS_AND_CONV
Conv.EXISTS_AND_CONV : conv
Moves an existential quantification inwards through a conjunction.
When applied to a term of the form ?x. P /\ Q, where x is not free
in both P and Q, EXISTS_AND_CONV returns a theorem of one of three
forms, depending on occurrences of the variable x in P and Q. If
x is free in P but not in Q, then the theorem:
|- (?x. P /\ Q) = (?x.P) /\ Q
is returned. If x is free in Q but not in P, then the result is:
|- (?x. P /\ Q) = P /\ (?x.Q)
And if x is free in neither P nor Q, then the result is:
|- (?x. P /\ Q) = (?x.P) /\ (?x.Q)
Failure
EXISTS_AND_CONV fails if it is applied to a term not of the form
?x. P /\ Q, or if it is applied to a term ?x. P /\ Q in which the
variable x is free in both P and Q.
See also
Conv.AND_EXISTS_CONV,
Conv.EXISTS_AND_REORDER_CONV,
Conv.LEFT_AND_EXISTS_CONV,
Conv.RIGHT_AND_EXISTS_CONV