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LEFT_AND_PEXISTS_CONV                                      (PairRules)
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LEFT_AND_PEXISTS_CONV : conv

KEYWORDS
conversion, quantifier, existential, conjunction.

LIBRARY
pair

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

DESCRIBE
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}.

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

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