An exact proof term for the current goal is (λH1 H2 H3 H4 H5 H6 H7 ⇒ andI (P1 ∧ P2 ∧ P3 ∧ P4 ∧ P5 ∧ P6) P7 (and6I H1 H2 H3 H4 H5 H6) H7).