formal/hol/Help/BINDER_CONV.doc

\DOC BINDER_CONV

\TYPE {BINDER_CONV : conv -> term -> thm}

\SYNOPSIS
Applies conversion to the body of a binder.

\DESCRIBE
If {c} is a conversion such that {c `t`} returns {|- t = t'}, then
{BINDER_CONV c `b (\x. t)`} returns {|- b (\x. t) = b (\x. t')}, i.e. applies
the core conversion to the body of a `binder'. In fact, {b} here can be any
term, but it is typically a binder constant such as a quantifier.

\FAILURE
Fails if the core conversion does, or if the theorem returned by it is not of
the right form.

\EXAMPLE
{
  # BINDER_CONV SYM_CONV `@n. n = m + 1`;;
  val it : thm = |- (@n. n = m + 1) = (@n. m + 1 = n)

  # BINDER_CONV (REWR_CONV SWAP_FORALL_THM) `!x y z. x + y + z = y + x + z`;;
  val it : thm =
    |- (!x y z. x + y + z = y + x + z) <=> (!x z y. x + y + z = y + x + z)
}

\SEEALSO
ABS_CONV, RAND_CONV, RATOR_CONV.

\ENDDOC