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\DOC NUM_EVEN_CONV
\TYPE {NUM_EVEN_CONV : conv}
\SYNOPSIS
Proves whether a natural number numeral is even.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} is a numeral (e.g. {0}, {1}, {2}, {3},...), then {NUM_EVEN_CONV `n`}
returns one of the theorems:
{
|- EVEN(n) <=> T
}
\noindent or
{
|- EVEN(n) <=> F
}
\noindent according to whether the number denoted by {n} is even.
\FAILURE
Fails if applied to a term that is not of the form {`EVEN n`} with {n} a
numeral.
\EXAMPLE
{
# NUM_EVEN_CONV `EVEN 99`;;
val it : thm = |- EVEN 99 <=> F
# NUM_EVEN_CONV `EVEN 123456`;;
val it : thm = |- EVEN 123456 <=> T
}
\SEEALSO
NUM_ADD_CONV, NUM_DIV_CONV, NUM_EQ_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_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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