\DOC ALPHA_CONV

\TYPE {ALPHA_CONV : term -> term -> thm}

\SYNOPSIS
Renames the bound variable of a lambda-abstraction.

\KEYWORDS
conversion, alpha.

\DESCRIBE
If {`y`} is a variable of type {ty} and {`\x. t`} is an abstraction in which
the bound variable {x} also has type {ty} and {y} does not occur free in {t},
then {ALPHA_CONV `y` `\x. t`} returns the theorem:
{
   |- (\x. t) = (\y. t[y/x])
}

\FAILURE
Fails if the first argument is not a variable, the second is not an
abstraction, if the types of the new variable and the bound variable in the
abstraction differ, or if the new variable is already free in the body of the
abstraction.

\EXAMPLE
{
  # ALPHA_CONV `y:num` `\x. x + 1`;;
  val it : thm = |- (\x. x + 1) = (\y. y + 1)

  # ALPHA_CONV `y:num` `\x. x + y`;;
  Exception: Failure "alpha: Invalid new variable".
}

\SEEALSO
ALPHA, GEN_ALPHA_CONV.

\ENDDOC