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\DOC NUM_FACT_CONV
\TYPE {NUM_FACT_CONV : term -> thm}
\SYNOPSIS
Proves what the factorial of a natural number numeral is.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} is a numeral (e.g. {0}, {1}, {2}, {3},...), then
{NUM_FACT_CONV `FACT n`} returns the theorem:
{
|- FACT n = s
}
\noindent where {s} is the numeral that denotes the factorial of the natural
number denoted by {n}.
\FAILURE
{NUM_FACT_CONV tm} fails if {tm} is not of the form {`FACT n`}, where {n} is a
numeral.
\EXAMPLE
{
# NUM_FACT_CONV `FACT 0`;;
val it : thm = |- FACT 0 = 1
# NUM_FACT_CONV `FACT 6`;;
val it : thm = |- FACT 6 = 720
# NUM_FACT_CONV `FACT 30`;;
val it : thm = |- FACT 30 = 265252859812191058636308480000000
}
\SEEALSO
NUM_ADD_CONV, NUM_DIV_CONV, NUM_EQ_CONV, NUM_EVEN_CONV, NUM_EXP_CONV,
NUM_GE_CONV, NUM_GT_CONV, NUM_LE_CONV, NUM_LT_CONV, NUM_MAX_CONV, NUM_MIN_CONV,
NUM_MOD_CONV, NUM_MULT_CONV, NUM_ODD_CONV, NUM_PRE_CONV, NUM_REDUCE_CONV,
NUM_RED_CONV, NUM_REL_CONV, NUM_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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