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\DOC REAL_LE_IMP
\TYPE {REAL_LE_IMP : thm -> thm}
\SYNOPSIS
Perform transitivity chaining for non-strict real number inequality.
\DESCRIBE
When applied to a theorem {A |- s <= t} where {s} and {t} have type {real}, the
rule {REAL_LE_IMP} returns {A |- !x1...xn z. t <= z ==> s <= z}, where {z} is
some variable and the {x1,...,xn} are free variables in {s} and {t}.
\FAILURE
Fails if applied to a theorem whose conclusion is not of the form {`s <= t`}
for some real number terms {s} and {t}.
\EXAMPLE
{
# REAL_LE_IMP (REAL_ARITH `x:real <= abs(x)`);;
val it : thm = |- !x z. abs x <= z ==> x <= z
}
\USES
Can make transitivity chaining in goals easier, e.g. by
{FIRST_ASSUM(MATCH_MP_TAC o REAL_LE_IMP)}.
\SEEALSO
LE_IMP, REAL_ARITH, REAL_LET_IMP.
\ENDDOC
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