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\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
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