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Proof step 26 from proof refine-change (previous step)

# apebs0 = # wlar0, # apebs = # wlar, LEB_SIZE = n2 + n, apebs0[n0] = mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n2), 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(n2), n)]], apebs0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], q0), VTBL_VOLID ∈ vols, q0.lebrefs ⊆ q.lebrefs ++ (v × vtblpnum) ∧ abs(avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]], apebs0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], q) ∧ v ∈ avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]] ∧ vtblpnum < # avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]][v] ∧ avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]][v][vtblpnum] ≠ erased

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# apebs = # wlar, # apebs0 = # wlar0, LEB_SIZE = n2 + n, apebs0[n0] = mkpeb(aehdr, avhdr, subarray(buf, 0, n) + mkempbuf(n2), align↑(datasize(buf, n), EB_PAGE_SIZE), boolvar), vtblpnum < # avols[v], vtblpnum < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-ebatbl(apebs0, wlar0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), v ∈ avols, v ∈ vols, n ≤ LEB_SIZE, n ≤ # buf, 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)) ⊦ abs(avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]], apebs0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], q0), abs(avols[v, avols[v][vtblpnum, mapped(subarray(buf, 0, n) + mkempbuf(n2), n)]], apebs0, vols[v, vols[v][vtblpnum, ⌜n0⌝ ]], q), VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ erased ≠ mapped(buf, m); (s)% ⊦ m < # evol → evol[m, leb][m] = leb; (s)%⊦ v ∈ vols ∧ m < # vols[v] ∧ abs(avols, apebs, vols, q) → m < # avols[v]; (ss)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ avols[v, evol][v] = evol; (s)% ⊦ v ∈ avols[v, evol]; (s)