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Proof step 21 from proof refine-change (previous step)

# apebs0 = # wlar0, # apebs = # wlar, LEB_SIZE = n1 + n, apebs0[n0] = mkpeb(aehdr, avhdr, buf0, m, boolvar), err = err1, err = ESUCCESS, vtblpnum < # vols[v], vtblpnum < # avols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum1), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, 0 + n ≤ # buf, n ≤ # buf, n ≤ LEB_SIZE, LEB_SIZE ≥ n, err1 ≠ ESUCCESS → vols0 = vols ∧ id(apebs0, apebs, mapped-pebs(vols)) ∧ q0.lebrefs ⊆ q.lebrefs, err1 = ESUCCESS → q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum) ∧ (vols[v][vtblpnum] ≠ unmapped → id(apebs0, apebs, mapped-pebs(vols) -- vols[v][vtblpnum].pnum)) ∧ (vols[v][vtblpnum] = unmapped → id(apebs0, apebs, mapped-pebs(vols))) ∧ vols0 = vols[v, vols[v][vtblpnum, ⌜n0⌝ ]] ∧ buf0 = subarray(buf, 0, n) + mkempbuf(n1) ∧ m = align↑(datasize(buf, n), EB_PAGE_SIZE), err1 = ESUCCESS ∨ ⌊err1⌋ ⊦ VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols, abs(avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(LEB_SIZE - n), n)]], apebs0, vols0, q0) ∧ err1 = err

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# apebs0 = # wlar0, # apebs = # wlar, LEB_SIZE = n1 + n, apebs0[n0] = mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n1), align↑(datasize(buf, n), EB_PAGE_SIZE), boolvar), vtblpnum < # vols[v], vtblpnum < # avols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], vtblpnum1), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, n ≤ # buf, n ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum), vols[v][vtblpnum] = unmapped → id(apebs0, apebs, mapped-pebs(vols)), vols[v][vtblpnum] ≠ unmapped → id(apebs0, apebs, mapped-pebs(vols) -- vols[v][vtblpnum].pnum) ⊦ abs(avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(LEB_SIZE - n), n)]], apebs0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], q0), VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ 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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)