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Proof step 26 from proof refine-wl-worker (previous step)

# apebs0 = # wlar0, # apebs = # wlar, apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar), apebs[vols[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), buf = buf0, vols0 = vols[v, vols[v][m, ⌜n⌝ ]], m < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- vols[v][m].pnum), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols0, 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, vols0, 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) ⊦ vols[v][m] = unmapped, abs(avols, apebs0, vols0, q0), VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# 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?, avhdr0.valid?, n0 < # wlar, m < # vols[v], abs(avols, apebs, vols, q), 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

Rule argument

Additional information

Used simplifier rules: lf-elim-unmapped: ⊦ vols[v][m] ≠ unmapped → (∃ n. vols[v][m] = ⌜n⌝ );%lf-mapped-in-apebs: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → n < # apebs;%lf-mapped-valid-vidhdr: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar) → avhdr.valid?;%lf-mapped-not-bad: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-wl(apebs, wlar) ∧ apebs[n] = mkpeb(aehdr, avhdr, buf, m0, boolvar) → ¬ boolvar;%ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ unmapped ≠ ⌜m⌝ ; (s)% ⊦ ⌜m⌝ .pnum = m; (s)%abs-vols-mapped: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ abs(avols, apebs, vols, q) → avols[v][m].mapped?; (forward) from specification ubi-abs% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)%⊦ v ∈ vols → ( valid-vtbl(apebs, vols[v, vols[v][m, ebae]], wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)