FORALL_OR_CONV
Conv.FORALL_OR_CONV : conv
Moves a universal quantification inwards through a disjunction.
When applied to a term of the form !x. P \/ Q, where x is not free
in both P and Q, FORALL_OR_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
FORALL_OR_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.OR_FORALL_CONV,
Conv.LEFT_OR_FORALL_CONV,
Conv.RIGHT_OR_FORALL_CONV