LEFT_AND_PEXISTS_CONV

PairRules.LEFT_AND_PEXISTS_CONV : conv

Moves a paired existential quantification of the left conjunct outwards through a conjunction.

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

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

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

Failure

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

See also

Conv.LEFT_AND_EXISTS_CONV, PairRules.AND_PEXISTS_CONV, PairRules.PEXISTS_AND_CONV, PairRules.RIGHT_AND_PEXISTS_CONV