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\DOC NUM_PRE_CONV
\TYPE {NUM_PRE_CONV : term -> thm}
\SYNOPSIS
Proves what the cutoff predecessor of a natural number numeral is.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} is a numeral (e.g. {0}, {1}, {2}, {3},...), then
{NUM_PRE_CONV `PRE n`} returns the theorem:
{
|- PRE n = s
}
\noindent 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
{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
}
\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_REDUCE_CONV, NUM_RED_CONV, NUM_REL_CONV, NUM_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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