OR_FORALL_CONV

Conv.OR_FORALL_CONV : conv

Moves a universal quantification outwards through a disjunction.

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.

See also

Conv.FORALL_OR_CONV, Conv.LEFT_OR_FORALL_CONV, Conv.RIGHT_OR_FORALL_CONV