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RIGHT_IMP_PFORALL_CONV                                     (PairRules)
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RIGHT_IMP_PFORALL_CONV : conv

KEYWORDS
conversion, quantifier, universal, implication.

LIBRARY
pair

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

DESCRIBE
When applied to a term of the form {t ==> (!p. u)}, the conversion
{RIGHT_IMP_FORALL_CONV} returns the theorem:

   |- t ==> (!p. u) = (!p'. t ==> (u[p'/p]))

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 {t ==> (!p. u)}.

SEEALSO
Conv.RIGHT_IMP_FORALL_CONV, PairRules.PFORALL_IMP_CONV,
PairRules.LEFT_IMP_PEXISTS_CONV.

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