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Theorem step-M10-M13

⊦ ( (# gs.ar ≠ 0 ∧ htok(gs.ar)) ∧ ls.n < # gs.ar ∧ ls.e ≠ ⊥ ∧ ls.sz = # gs.ar ∧ (ls.n0 < # gs.ar ∧ ls.n0 = get_hash(ls.e, ls.sz)) ∧ ¬ ls.b ∧ (ls.e0 ≠ ⊥ → ls.e0 = gs.ar[ls.n]) ∧ ls.e ≠ ls.e0 ∧ allslotsfull(gs.ar, ls.n0, ls.n, ls.e, false)) ∧ pre(gs, ls, M10, a) ∧ pcstepf(gs, ls, M10, a) = M13 → (# gstepf(gs, ls, M10, a).ar ≠ 0 ∧ htok(gstepf(gs, ls, M10, a).ar)) ∧ lstepf(gs, ls, M10, a).n < # gstepf(gs, ls, M10, a).ar ∧ lstepf(gs, ls, M10, a).e ≠ ⊥ ∧ lstepf(gs, ls, M10, a).sz = # gstepf(gs, ls, M10, a).ar ∧ ( lstepf(gs, ls, M10, a).n0 < # gstepf(gs, ls, M10, a).ar ∧ lstepf(gs, ls, M10, a).n0 = get_hash(lstepf(gs, ls, M10, a).e, lstepf(gs, ls, M10, a).sz)) ∧ ¬ lstepf(gs, ls, M10, a).b ∧ (gstepf(gs, ls, M10, a).ar[lstepf(gs, ls, M10, a).n] ≠ ⊥ ∧ gstepf(gs, ls, M10, a).ar[lstepf(gs, ls, M10, a).n] ≠ lstepf(gs, ls, M10, a).e) ∧ lstepf(gs, ls, M10, a).e ≠ lstepf(gs, ls, M10, a).e0 ∧ allslotsfull(gstepf(gs, ls, M10, a).ar, lstepf(gs, ls, M10, a).n0, lstepf(gs, ls, M10, a).n, lstepf(gs, ls, M10, a).e, false)

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