Strong tree Properties for two successive cardinals

An inaccessible cardinal $κ$ is supercompact when $(κ, λ)$-ITP holds for all $λ\geq κ.$ We prove that if there is a model of $\ZFC$ with two supercompact cardinals, then there is a model of \ZFC where simultaneously $(\aleph_2, μ)$-ITP and $(\aleph_3, μ')$-ITP hold, for all $μ\geq \aleph_2$ and $μ'\geq \aleph_3.$

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