AND_PEXISTS_CONV

PairRules.AND_PEXISTS_CONV : conv

Moves a paired existential quantification outwards through a conjunction.

When applied to a term of the form (?p. t) /\ (?p. u), where no variables in p are free in either t or u, AND_PEXISTS_CONV returns the theorem:

   |- (?p. t) /\ (?p. u) = (?p. t /\ u)

Failure

AND_PEXISTS_CONV fails if it is applied to a term not of the form (?p. t) /\ (?p. u), or if it is applied to a term (?p. t) /\ (?p. u) in which variables from p are free in either t or u.

See also

Conv.AND_EXISTS_CONV, PairRules.PEXISTS_AND_CONV, PairRules.LEFT_AND_PEXISTS_CONV, PairRules.RIGHT_AND_PEXISTS_CONV