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LEFT_IMP_PFORALL_CONV                                      (PairRules)
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LEFT_IMP_PFORALL_CONV : conv

KEYWORDS
conversion, quantifier, universal, implication.

LIBRARY
pair

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

DESCRIBE
When applied to a term of the form {(!p. t) ==> u}, the conversion
{LEFT_IMP_PFORALL_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_FORALL_CONV, PairRules.PEXISTS_IMP_CONV,
PairRules.RIGHT_IMP_PFORALL_CONV.

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