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\DOC NUM_EQ_CONV
\TYPE {NUM_EQ_CONV : conv}
\SYNOPSIS
Proves equality or inequality of two numerals.
\KEYWORDS
conversion, number, arithmetic.
\DESCRIBE
If {n} and {m} are two numerals (e.g. {0}, {1}, {2}, {3},...), then
{NUM_EQ_CONV `n = m`} returns:
{
|- (n = m) <=> T or |- (n = m) <=> F
}
\noindent depending on whether the natural numbers represented by {n} and {m}
are equal or not equal, respectively.
\FAILURE
{NUM_EQ_CONV tm} fails if {tm} is not of the form {`n = m`}, where {n} and {m}
are numerals.
\EXAMPLE
{
# NUM_EQ_CONV `1 = 2`;;
val it : thm = |- 1 = 2 <=> F
# NUM_EQ_CONV `12 = 12`;;
val it : thm = |- 12 = 12 <=> T
}
\USES
Performing basic arithmetic reasoning while producing a proof.
\SEEALSO
NUM_ADD_CONV, NUM_DIV_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_PRE_CONV, NUM_REDUCE_CONV,
NUM_RED_CONV, NUM_REL_CONV, NUM_SUB_CONV, NUM_SUC_CONV.
\ENDDOC
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