AND_FORALL_CONV

Conv.AND_FORALL_CONV : conv

Moves a universal quantification outwards through a conjunction.

When applied to a term of the form (!x.P) /\ (!x.Q), the conversion AND_FORALL_CONV returns the theorem:

   |- (!x.P) /\ (!x.Q) = (!x. P /\ Q)

Failure

Fails if applied to a term not of the form (!x.P) /\ (!x.Q).

Comments

It may be easier to use higher order rewriting with FORALL_AND_THM.

See also

Conv.FORALL_AND_CONV, Conv.LEFT_AND_FORALL_CONV, Conv.RIGHT_AND_FORALL_CONV