\DOC PSPEC
\TYPE {PSPEC : (term -> thm -> thm)}
\KEYWORDS
rule.
\LIBRARY pair
\SYNOPSIS
Specializes the conclusion of a theorem.
\DESCRIBE
When applied to a term {q} and a theorem {A |- !p. t}, then {PSPEC}
returns
the theorem {A |- t[q/p]}.
If necessary, variables will be renamed prior to the specialization to
ensure
that {q} is free for {p} in {t}, that is,
no variables free in {q} become bound after substitution.
{
A |- !p. t
-------------- PSPEC "q"
A |- t[q/p]
}
\FAILURE
Fails if the theorem's conclusion is not a paired universal
quantification,
or if {p} and {q} have different types.
\EXAMPLE
{PSPEC} specialised paired quantifications.
{
#PSPEC "(1,2)" (ASSUME "!(x,y). (x + y) = (y + x)");;
. |- 1 + 2 = 2 + 1
}
{PSPEC} treats paired structures of variables as variables and
preserves structure accordingly.
{
#PSPEC "x:*#*" (ASSUME "!(x:*,y:*). (x,y) = (x,y)");;
. |- x = x
}
\SEEALSO
SPEC, IPSPEC, PSPECL, PSPEC_ALL, PSPEC_VAR, PGEN, PGENL, PGEN_ALL.
\ENDDOC