SPEC : (term -> thm -> thm)

SYNOPSIS

Specializes the conclusion of a theorem.

DESCRIBE

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

Fails if the theorem's conclusion is not universally quantified, or if x and u have different types.

EXAMPLE

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);;
   |- !x. x ==> (!y. y ==> x)

   #SPEC "~y" it;;
   |- ~y ==> (!y'. y' ==> ~y)

SEEALSO  ISPEC,   SPECL,   SPEC_ALL,   SPEC_VAR,   GEN,   GENL,   GEN_ALL