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FORALL_OR_CONV                                                  (Conv)
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FORALL_OR_CONV : conv

SYNOPSIS
Moves a universal quantification inwards through a disjunction.

KEYWORDS
conversion, quantifier, universal, disjunction.

DESCRIBE
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}.

SEEALSO
Conv.OR_FORALL_CONV, Conv.LEFT_OR_FORALL_CONV,
Conv.RIGHT_OR_FORALL_CONV.

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