NUM_FACT_CONV : term -> thm

SYNOPSIS

Proves what the factorial of a natural number numeral is.

DESCRIPTION

If n is a numeral (e.g. 0, 1, 2, 3,...), then NUM_FACT_CONV `FACT n` returns the theorem:

   |- FACT n = s

where s is the numeral that denotes the factorial of the natural number denoted by n.

FAILURE CONDITIONS

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

SEE ALSO

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.