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LEFT_IMP_PEXISTS_CONV                                      (PairRules)
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LEFT_IMP_PEXISTS_CONV : conv

KEYWORDS
conversion, quantifier, existential, implication.

SYNOPSIS
Moves a paired existential quantification of the antecedent outwards through
an implication.

DESCRIBE
When applied to a term of the form {(?p. t) ==> u}, the conversion
{LEFT_IMP_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
contain any variables that appear free in the input term.

FAILURE
Fails if applied to a term not of the form {(?p. t) ==> u}.

SEEALSO
Conv.LEFT_IMP_EXISTS_CONV, PairRules.PFORALL_IMP_CONV,
PairRules.RIGHT_IMP_PFORALL_CONV.

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