Perform transitivity chaining for mixed strict/non-strict real number
inequality.
DESCRIPTION
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 CONDITIONS
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_LET_IMP (REAL_ARITH `abs(x + y) <= abs(x) + abs(y)`);;
val it : thm = |- !x y z. abs x + abs y < z ==> abs (x + y) < z
USES
Can make transitivity chaining in goals easier, e.g. by
FIRST_ASSUM(MATCH_MP_TAC o REAL_LE_IMP).