1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
|
\DOC NUM_SUB_CONV
\TYPE {NUM_SUB_CONV : term -> thm}
\SYNOPSIS
Proves what the cutoff difference of two natural number numerals is.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} and {m} are numerals (e.g. {0}, {1}, {2}, {3},...), then
{NUM_SUB_CONV `n - m`} returns the theorem:
{
|- n - m = s
}
\noindent 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
{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}.
\SEEALSO
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_PRE_CONV, NUM_REDUCE_CONV, NUM_RED_CONV, NUM_REL_CONV, NUM_SUC_CONV.
\ENDDOC
|
