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\DOC NUM_EXP_CONV
\TYPE {NUM_EXP_CONV : term -> thm}
\SYNOPSIS
Proves what the exponential 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_EXP_CONV `n EXP m`} returns the theorem:
{
|- n EXP m = s
}
\noindent where {s} is the numeral that denotes the natural number denoted by
{n} raised to the power of the one denoted by {m}.
\FAILURE
{NUM_EXP_CONV tm} fails if {tm} is not of the form {`n EXP m`}, where {n} and
{m} are numerals.
\EXAMPLE
{
# NUM_EXP_CONV `2 EXP 64`;;
val it : thm = |- 2 EXP 64 = 18446744073709551616
# NUM_EXP_CONV `1 EXP 99`;;
val it : thm = |- 1 EXP 99 = 1
# NUM_EXP_CONV `0 EXP 0`;;
val it : thm = |- 0 EXP 0 = 1
# NUM_EXP_CONV `0 EXP 10000`;;
val it : thm = |- 0 EXP 10000 = 0
}
\SEEALSO
NUM_ADD_CONV, NUM_DIV_CONV, NUM_EQ_CONV, NUM_EVEN_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_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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