File: OR_FORALL_CONV.doc

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\DOC OR_FORALL_CONV

\TYPE {OR_FORALL_CONV : conv}

\SYNOPSIS
Moves a universal quantification outwards through a disjunction.

\KEYWORDS
conversion, quantifier, universal, disjunction.

\DESCRIBE
When applied to a term of the form {(!x.P) \/ (!x.Q)}, where {x} is free
in neither {P} nor {Q}, {OR_FORALL_CONV} returns the theorem:
{
   |- (!x. P) \/ (!x. Q) = (!x. P \/ Q)
}
\FAILURE
{OR_FORALL_CONV} fails if it is applied to a term not of the form
{(!x.P) \/ (!x.Q)}, or if it is applied to a term {(!x.P) \/ (!x.Q)}
in which the variable {x} is free in either {P} or {Q}.

\SEEALSO
FORALL_OR_CONV, LEFT_OR_FORALL_CONV, RIGHT_OR_FORALL_CONV.

\ENDDOC