\DOC ABS

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

\SYNOPSIS
Abstracts both sides of an equation.

\KEYWORDS
rule, abstraction.

\DESCRIBE
{
         A |- t1 = t2
   ------------------------  ABS `x`            [Where x is not free in A]
    A |- (\x.t1) = (\x.t2)
}

\FAILURE
If the theorem is not an equation, or if the variable {x} is free in the
assumptions {A}.

\EXAMPLE
{
  # ABS `m:num` (REFL `m:num`);;
  val it : thm = |- (\m. m) = (\m. m)
}

\COMMENTS
This is one of HOL Light's 10 primitive inference rules.

\SEEALSO
ETA_CONV.

\ENDDOC