NUM_SUB_CONV : term -> thm

SYNOPSIS

Proves what the cutoff difference of two natural number numerals is.

DESCRIPTION

If n and m are numerals (e.g. 0, 1, 2, 3,...), then NUM_SUB_CONV `n - m` returns the theorem:

   |- n - m = s

where s is the numeral that denotes the result of subtracting the natural number denoted by m from the one denoted by n, returning zero for all cases where m is greater than n (cutoff subtraction over the natural numbers).

FAILURE CONDITIONS

NUM_SUB_CONV tm fails if tm is not of the form `n - m`, where n and m are numerals.

EXAMPLE

  # NUM_SUB_CONV `4321 - 1234`;;
  val it : thm = |- 4321 - 1234 = 3087

  # NUM_SUB_CONV `77 - 88`;;
  val it : thm = |- 77 - 88 = 0

COMMENTS

Note that subtraction over type :num is defined as this cutoff subtraction. If you want a number system with negative numbers, use :int or :real.