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Theorem step-M3-M4

⊦ ((# gs.ar ≠ 0 ∧ htok(gs.ar)) ∧ ls.e ≠ ⊥ ∧ ls.sz = # gs.ar ∧ ls.n0 < # gs.ar ∧ ls.n0 = get_hash(ls.e, ls.sz)) ∧ pre(gs, ls, M3, a) ∧ pcstepf(gs, ls, M3, a) = M4 → (# gstepf(gs, ls, M3, a).ar ≠ 0 ∧ htok(gstepf(gs, ls, M3, a).ar)) ∧ lstepf(gs, ls, M3, a).n < # gstepf(gs, ls, M3, a).ar ∧ lstepf(gs, ls, M3, a).e ≠ ⊥ ∧ lstepf(gs, ls, M3, a).sz = # gstepf(gs, ls, M3, a).ar ∧ ( lstepf(gs, ls, M3, a).n0 < # gstepf(gs, ls, M3, a).ar ∧ lstepf(gs, ls, M3, a).n0 = get_hash(lstepf(gs, ls, M3, a).e, lstepf(gs, ls, M3, a).sz)) ∧ lstepf(gs, ls, M3, a).n = lstepf(gs, ls, M3, a).n0 ∧ allslotsfull(gstepf(gs, ls, M3, a).ar, lstepf(gs, ls, M3, a).n0, lstepf(gs, ls, M3, a).n, lstepf(gs, ls, M3, a).e, false)

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