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\DOC GENL
\TYPE {GENL : term list -> thm -> thm}
\SYNOPSIS
Generalizes zero or more variables in the conclusion of a theorem.
\KEYWORDS
rule, quantifier, universal.
\DESCRIBE
When applied to a term list {[x1;...;xn]} and a theorem {A |- t}, the inference
rule {GENL} returns the theorem {A |- !x1...xn. t}, provided none of the
variables {xi} are free in any of the assumptions. It is not necessary that
any or all of the {xi} should be free in {t}.
{
A |- t
------------------ GENL `[x1;...;xn]` [where no xi is free in A]
A |- !x1...xn. t
}
\FAILURE
Fails unless all the terms in the list are variables, none of which are
free in the assumption list.
\EXAMPLE
{
# SPEC `m + p:num` ADD_SYM;;
val it : thm = |- !n. (m + p) + n = n + m + p
# GENL [`m:num`; `p:num`] it;;
val it : thm = |- !m p n. (m + p) + n = n + m + p
}
\SEEALSO
GEN, GEN_ALL, GEN_TAC, SPEC, SPECL, SPEC_ALL, SPEC_TAC.
\ENDDOC
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