\DOC SPECL
\TYPE {SPECL : term list -> thm -> thm}
\SYNOPSIS
Specializes zero or more variables in the conclusion of a theorem.
\KEYWORDS
rule.
\DESCRIBE
When applied to a term list {[u1;...;un]} and a theorem
{A |- !x1...xn. t}, the inference rule {SPECL} returns the theorem
{A |- t[u1/x1]...[un/xn]}, where the substitutions are made
sequentially left-to-right in the same way as for {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...xn. t
-------------------------- SPECL [u1,...,un]
A |- t[u1/x1]...[un/xn]
}
It is permissible for the term-list to be empty, in which case
the application of {SPECL} has no effect.
\FAILURE
Fails unless each of the terms is of the same type as that of the
appropriate quantified variable in the original theorem.
\EXAMPLE
The following is a specialization of a theorem from theory {arithmetic}.
{
- arithmeticTheory.LESS_EQ_LESS_EQ_MONO;
> val it = |- !m n p q. m <= p /\ n <= q ==> m + n <= p + q : thm
- SPECL (map Term [`1`, `2`, `3`, `4`]) it;
> val it = |- 1 <= 3 /\ 2 <= 4 ==> 1 + 2 <= 3 + 4 : thm
}
\SEEALSO
Thm.GEN, Drule.GENL, Drule.GEN_ALL, Tactic.GEN_TAC, Thm.SPEC,
Drule.SPEC_ALL, Tactic.SPEC_TAC.
\ENDDOC