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\DOC NUM_LE_CONV
\TYPE {NUM_LE_CONV : conv}
\SYNOPSIS
Proves whether one numeral is less than or equal to another.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} and {m} are two numerals (e.g. {0}, {1}, {2}, {3},...), then
{NUM_LE_CONV `n <= m`} returns:
{
|- n <= m <=> T or |- n <= m <=> F
}
\noindent depending on whether the natural number represented by {n} is less
than or equal to the one represented by {m}.
\FAILURE
{NUM_LE_CONV tm} fails if {tm} is not of the form {`n <= m`}, where {n} and {m}
are numerals.
\EXAMPLE
{
# NUM_LE_CONV `12 <= 19`;;
val it : thm = |- 12 <= 19 <=> T
# NUM_LE_CONV `12345 <= 12344`;;
val it : thm = |- 12345 <= 12344 <=> F
}
\USES
Performing basic arithmetic reasoning while producing a proof.
\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_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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