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Proof step 30 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?, 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, abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q) ∧ avols[v][m] ≠ erased

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ abs○(avols, apebs, vols, q, v, m) ∧ v ∈ vols ∧ m < # vols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ vols[v][m] = ⌜n⌝ ∧ apebs[n].data = buf ∧ apebs[n].fill ≤ m0 → abs(avols, apebs, vols, q)
Proof step 32:
# apebs = # wlar, # apebs0 = # wlar0, apebs0[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), vols[v][m] = ⌜n0⌝ , apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m1, false), avols[v][m].mapped?, avhdr0.valid?, m < # vols[v], n0 < # wlar, abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- n0), ubi-io-inv(apebs), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf0, m1, false)), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][m, ⌜n⌝ ]], vtblpnum0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum0), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), v ∈ vols, m0 ≤ m1, q0.lebrefs ⊆ q.lebrefs ++ (v × m) ⊦ abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q0), VTBL_VOLID ∈ vols, abs(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q) ∧ avols[v][m] ≠ erased, abs○(avols, apebs0, vols[v, vols[v][m, ⌜n⌝ ]], q, v, m) ∧ v ∈ vols[v, vols[v][m, ⌜n⌝ ]] ∧ m < # vols[v, vols[v][m, ⌜n⌝ ]][v] ∧ avols[v][m] = mapped(apebs0[n].data, avols[v][m].fill) ∧ vols[v, vols[v][m, ⌜n⌝ ]][v][m] = ⌜n⌝ ∧ apebs0[n].data = apebs0[n].data ∧ apebs0[n].fill ≤ avols[v][m].fill

Rule argument

spec: ubi-abs name: absexpt-mapped-abs seq: ⊦ abs○(avols, apebs, vols, q, v, m) ∧ v ∈ vols ∧ m < # vols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ vols[v][m] = ⌜n⌝ ∧ apebs[n].data = buf ∧ apebs[n].fill ≤ m0 → abs(avols, apebs, vols, q) subst: [v, m, buf, m0, n, q, vols, apebs, avols] → [v, m, apebs0[n].data, avols[v][m].fill, n, q, vols[v, vols[v][m, ⌜n⌝ ]], apebs0, avols] flags: <all paths>

Additional information

Used simplifier rules: ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ m < # ebatbl → ebatbl[m, ebae][m] = ebae; (s)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)% ⊦ v ∈ vols[v, ebatbl]; (s)% ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ erased.fill = 0; (s)% ⊦ erased ≠ mapped(buf, m); (s) Used terms: v, m, apebs0[n].data, avols[v][m].fill, n, q, vols[v, vols[v][m, ⌜n⌝ ]], apebs0, avols