SPEC : term -> thm -> thm
Specializes the conclusion of a theorem.
When applied to a term u and a theorem A |- !x. t, then SPEC returns
the theorem A |- t[u/x]. If necessary, variables will be renamed prior
to the specialization to ensure that u is free for x in t, that is,
no variables free in u become bound after substitution.
A |- !x. t
-------------- SPEC `u`
A |- t[u/x]
- FAILURE CONDITIONS
Fails if the theorem's conclusion is not universally quantified, or if x and
u have different types.
The following example shows how SPEC renames bound variables if necessary,
prior to substitution: a straightforward substitution would result in the
clearly invalid theorem |- ~y ==> (!y. y ==> ~y).
# let xv = `x:bool` and yv = `y:bool` in
(GEN xv o DISCH xv o GEN yv o DISCH yv) (ASSUME xv);;
val it : thm = |- !x. x ==> (!y. y ==> x)
# SPEC `~y` it;;
val it : thm = |- ~y ==> (!y'. y' ==> ~y)
In order to specialize variables while also instantiating types of polymorphic
variables, use ISPEC instead.
- SEE ALSO
GEN, GENL, GEN_ALL, ISPEC, ISPECL, SPECL, SPEC_ALL, SPEC_VAR.