NUM_PRE_CONV : term -> thm

SYNOPSIS

Proves what the cutoff predecessor of a natural number numeral is.

DESCRIPTION

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

   |- PRE n = s

where s is the numeral that denotes the cutoff predecessor of the natural number denoted by n (that is, the result of subtracting 1 from it, or zero if it is already zero).

FAILURE CONDITIONS

NUM_PRE_CONV tm fails if tm is not of the form `PRE n`, where n is a numeral.

EXAMPLE

  # NUM_PRE_CONV `PRE 0`;;
  val it : thm = |- PRE 0 = 0

  # NUM_PRE_CONV `PRE 12345`;;
  val it : thm = |- PRE 12345 = 12344

SEE ALSO

NUM_ADD_CONV, NUM_DIV_CONV, NUM_EQ_CONV, NUM_EVEN_CONV, NUM_EXP_CONV, NUM_FACT_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_REDUCE_CONV, NUM_RED_CONV, NUM_REL_CONV, NUM_SUB_CONV, NUM_SUC_CONV.