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\DOC NUM_ODD_CONV
\TYPE {NUM_ODD_CONV : conv}
\SYNOPSIS
Proves whether a natural number numeral is odd.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} is a numeral (e.g. {0}, {1}, {2}, {3},...), then {NUM_ODD_CONV `n`}
returns one of the theorems:
{
|- ODD(n) <=> T
}
\noindent or
{
|- ODD(n) <=> F
}
\noindent according to whether the number denoted by {n} is odd.
\FAILURE
Fails if applied to a term that is not of the form {`ODD n`} with {n} a
numeral.
\EXAMPLE
{
# NUM_ODD_CONV `ODD 123`;;
val it : thm = |- ODD 123 <=> T
# NUM_ODD_CONV `ODD 1234`;;
val it : thm = |- ODD 1234 <=> F
}
\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_PRE_CONV,
NUM_REDUCE_CONV, NUM_RED_CONV, NUM_REL_CONV, NUM_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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