RIGHT_AND_PFORALL_CONV

PairRules.RIGHT_AND_PFORALL_CONV : conv

Moves a paired universal quantification of the right conjunct outwards through a conjunction.

When applied to a term of the form t /\ (!p. u), the conversion RIGHT_AND_PFORALL_CONV returns the theorem:

   |- t /\ (!p. u) = (!p'. t /\ (u[p'/p]))

where p' is a primed variant of the pair p that does not contain any variables free in the input term.

Failure

Fails if applied to a term not of the form t /\ (!p. u).

See also

Conv.RIGHT_AND_FORALL_CONV, PairRules.AND_PFORALL_CONV, PairRules.PFORALL_AND_CONV, PairRules.LEFT_AND_PFORALL_CONV