\DOC AP_TERM

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

\SYNOPSIS
Applies a function to both sides of an equational theorem.

\KEYWORDS
rule.

\DESCRIBE
When applied to a term {f} and a theorem {A |- x = y}, the
inference rule {AP_TERM} returns the theorem {A |- f x = f y}.
{
      A |- x = y
   ----------------  AP_TERM `f`
    A |- f x = f y
}

\FAILURE
Fails unless the theorem is equational and the supplied term is a function
whose domain type is the same as the type of both sides of the equation.

\EXAMPLE
{
  # NUM_ADD_CONV `2 + 2`;;
  val it : thm = |- 2 + 2 = 4

  # AP_TERM `(+) 1` it;;
  val it : thm = |- 1 + 2 + 2 = 1 + 4
}

\SEEALSO
AP_THM, MK_COMB.

\ENDDOC