\DOC RESQ_SPECL
\TYPE {RESQ_SPECL : (term list -> thm -> thm)}
\SYNOPSIS
Specializes zero or more variables in the conclusion of a restricted
universally quantified theorem.
\KEYWORDS
rule, restricted quantifier.
\DESCRIBE
When applied to a term list {[u1;...;un]} and a theorem
{A |- !x1::P1. ... !xn::Pn. t}, the inference rule {RESQ_SPECL} returns
the theorem
{
A,P1 u1,...,Pn un |- t[u1/x1]...[un/xn]
}
where the substitutions are made
sequentially left-to-right in the same way as for {RESQ_SPEC}, with the
same
sort of alpha-conversions applied to {t} if necessary to ensure that no
variables which are free in {ui} become bound after substitution.
{
A |- !x1::P1. ... !xn::Pn. t
-------------------------------------------- RESQ_SPECL "[u1;...;un]"
A,P1 u1, ..., Pn un |- t[u1/x1]...[un/xn]
}
It is permissible for the term-list to be empty, in which case
the application of {RESQ_SPECL} has no effect.
\FAILURE
Fails if one of the specialization of the
restricted universally quantified variable in the original theorem fails.
\SEEALSO
RESQ_GEN, RESQ_GENL, RESQ_GEN_ALL, RESQ_GEN_TAC, RESQ_SPEC,
RESQ_SPEC_ALL.
\ENDDOC