formal/hol/Help/ALPHA_UPPERCASE.doc

\DOC ALPHA

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

\SYNOPSIS
Proves equality of alpha-equivalent terms.

\KEYWORDS
rule, alpha.

\DESCRIBE
When applied to a pair of terms {t1} and {t1'} which are
alpha-equivalent, {ALPHA} returns the theorem {|- t1 = t1'}.
{

   -------------  ALPHA `t1` `t1'`
    |- t1 = t1'
}
\FAILURE
Fails unless the terms provided are alpha-equivalent.

\EXAMPLE
{
  # ALPHA `!x:num. x = x` `!y:num. y = y`;;
  val it : thm = |- (!x. x = x) <=> (!y. y = y)

  # ALPHA `\w. w + z` `\z'. z' + z`;;
  val it : thm = |- (\w. w + z) = (\z'. z' + z)
}

\SEEALSO
aconv, ALPHA_CONV, GEN_ALPHA_CONV.

\ENDDOC