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Proof step 28 from proof ubi-cons-same-vtbl (previous step)

# wlar0 = # wlar1, # apebs = # wlar1, avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr0.sqn = avhdr.sqn, wlar0[n0] = wl-entry(m4, used), apebs[n0] = mkpeb(aechdr(m4), avhdr0, buf0, m3, false), apebs[m0] = mkpeb(aechdr(m2), avhdr, buf, m, false), wlar1[m0] = wl-entry(m2, used), n0 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols0), buf0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar1, vols1, m0), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m4), avhdr0, buf0, m3, false)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m2), avhdr, buf, m, false)), m0 < # apebs ∧ n0 < # apebs ∧ m0 ≠ n0 ∧ valid-peb(VTBL_VOLID, VTBL_LNUM, apebs[m0]) ∧ valid-peb(VTBL_VOLID, VTBL_LNUM, apebs[n0]) → (∃ bag. valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs) = bag ++ apebs[m0].vidhdr.sqn ++ apebs[n0].vidhdr.sqn) ⊦ n0 = m0, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# apebs = # wlar1, # wlar0 = # wlar1, avhdr0.sqn = avhdr.sqn, wlar1[m0] = wl-entry(m2, used), apebs[m0] = mkpeb(aechdr(m2), avhdr, buf, m, false), apebs[n0] = mkpeb(aechdr(m4), avhdr0, buf0, m3, false), wlar0[n0] = wl-entry(m4, used), valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs) = bag ++ avhdr.sqn ++ avhdr.sqn, m0 < # wlar1, n0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), is-encoded(to-vtbl(vols0), buf0), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-ebatbl(apebs, wlar1, vols1, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m2), avhdr, buf, m, false)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m4), avhdr0, buf0, m3, false)), (bag ++ avhdr.sqn).max ≤ avhdr.sqn ⊦ n0 = m0, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ∅ ≠ bag ++ n; (s)% ⊦ m = (bag ++ m).max ↔ ¬(bag ≠ ∅ ∧ m < bag.max); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)