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Proof step 34 from proof refine-wl-worker (previous step)

# apebs0 = # wlar0, # apebs = # wlar, apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), vols[v][m] = ⌜n0⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), avols[v][m] = mapped(buf, m2), avols[v][m].mapped?, avhdr0.valid?, n0 < # wlar, m < # vols[v], abs(avols, apebs, vols, q), abs○(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q, v, m), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- n0), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf0, m1, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][m, ⌜n⌝ ]], vtblpnum0), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum0), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, m0 ≤ m1, q0.lebrefs ⊆ q.lebrefs ++ (v × m) ⊦ abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q0), VTBL_VOLID ∈ vols, m0 ≤ m2 ∧ avols[v][m] = mapped(buf0, m2), abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q) ∧ avols[v][m] ≠ erased

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
# apebs0 = # wlar0, # apebs = # wlar, apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), vols[v][m] = ⌜n0⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), avols[v][m] = mapped(buf0, m2), avhdr0.valid?, n0 < # wlar, m < # vols[v], m2 < m0, m2 < m1, abs(avols, apebs, vols, q), abs○(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q, v, m), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- n0), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf0, m1, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][m, ⌜n⌝ ]], vtblpnum0), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum0), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, m0 ≤ m1, q0.lebrefs ⊆ q.lebrefs ++ (v × m) ⊦ abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q0), abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q), VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: lf-mapped-data: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar) ∧ avols[v][m] = mapped(buf1, m1) ∧ abs(avols, apebs, vols, q) → buf1 = buf0;% ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ erased ≠ mapped(buf, m); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mapped(buf, m).mapped?; (s)