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Proof step 54 from proof inv-create-volume (previous step)

# wlar0 = # wlar2, # buf0 = LEB_SIZE, # apebs0 = # wlar2, # apebs = # wlar, # apebs2 = # wlar2, apebs0[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar2[vtblpnum] = wl-entry(m, free), err = ESUCCESS, vols0 = vols, aehdr.valid?, vtblpnum < # wlar2, bflipset-cons(bflipset, wlar2), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), id(apebs0, apebs, mapped-pebs(vols)), id(apebs2, apebs0, mapped-pebs(vols)), id(apebs2, apebs, mapped-pebs(vols)), id○(apebs2, apebs0, vtblpnum), is-aligned(LEB_SIZE, EB_PAGE_SIZE), is-encoded(to-vtbl(vols)[v, n], buf0), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-inv(apebs2), unique-sqns(apebs0), unique-sqns(apebs), unique-sqns(apebs2), valid-ebatbl(apebs0, wlar2, vols, vtblpnum3), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-eraseq(wlar2, []), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs2, q1), valid-eraseq(wlar0, q1), valid-eraseq(q1), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs2, sqnum0), valid-vtbl(apebs0, vols, wlar2, vtblpnum3), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-wl(apebs0, wlar2), valid-wl(apebs, wlar), valid-wl(apebs2, wlar0), v ∈ vols[v, mkebatbl(n)], # to-vtbl(vols)[v, n] * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ LEB_SIZE, 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE, err = ESUCCESS → (∀ v0, m0. ¬ v0 ∈ vols ∧ to-vtbl(vols)[v, n] = to-vtbl(vols)[v0, m0] → valid-ebatbl(apebs2, wlar0, vols[v0, fill(mkebatbl(m0), unmapped)], vtblpnum0) ∧ valid-vtbl(apebs2, vols[v0, fill(mkebatbl(m0), unmapped)], wlar0, vtblpnum0)), to-vtbl(vols)[v, n] = to-vtbl(vols) ∨ err ≠ ESUCCESS → valid-ebatbl(apebs2, wlar0, vols, vtblpnum0) ∧ valid-vtbl(apebs2, vols, wlar0, vtblpnum0), err ≠ ESUCCESS → q1.lebrefs = ∅, err = ESUCCESS → apebs2[vtblpnum].fill = align↑(datasize(apebs2[vtblpnum].data, LEB_SIZE), EB_PAGE_SIZE) ∧ apebs2[vtblpnum].data = buf0 ∧ q1.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM), err = ESUCCESS → q1 = eq-entry(vtblpnum3, VTBL_VOLID × VTBL_LNUM) ', err = ESUCCESS ∨ ⌊err⌋ ⊦ v = VTBL_VOLID, vtblpnum3 = vtblpnum, v ∈ vols, vtblpnum3 ∈ q, VTBL_VOLID ∈ vols, ¬ VTBL_VOLID ∈ vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)] ∧ valid-ebatbl(apebs2, wlar0, vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)], vtblpnum0) ∧ valid-vtbl(apebs2, vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)], wlar0, vtblpnum0) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs2, apebs, mapped-pebs(vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)])) ∧ ( err = ESUCCESS → ¬ v ∈ vols0 ∧ vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)] = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q1.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q1.lebrefs ⊆ q.lebrefs ∧ vols[v, mkebatbl(n)][v, fill(vols[v, mkebatbl(n)][v], unmapped)] = vols0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ valid-eraseq(eqent '); (s)% ⊦ lref ∈ ∅ ++ lref0 ↔ lref = lref0; (s)% ⊦ ∅ ++ lref ⊆ s0 ↔ lref ∈ s0; (s)% ⊦ eq-entry(n, v × m) '.lebrefs = ∅ ++ (v × m); (s)%⊦ ¬ v ∈ vols ∧ ¬ v ∈ vols0 → (vols[v, ebatbl] = vols0[v, ebatbl] ↔ vols = vols0); (s)%⊦ ¬ v ∈ vols → mapped-pebs(vols[v, fill(mkebatbl(n), unmapped)]) = mapped-pebs(vols); (s)% ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s)% ⊦ vols[v, ebatbl][v, ebatbl0] = vols[v, ebatbl0]; (s)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)