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It is shown that the feasibly constructive arithmetic theory IPV
does not prove (double negation of) LMIN(NP), unless the
polynomial hierarchy CPV-provably collapses. It is proved that PV
plus (double negation of) LMIN(NP)intuitionistically proves
PIND(coNP). It is observed that PV+PIND(NP $\cup$ coNP) does not
intuitionistically prove NPB, a scheme which sates that the
extended Frege systems are not polynomially bounded.
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