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Proof step 26 from proof ubi-cons-same-vtbl (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, avhdr0.sqn = avhdr.sqn, avhdr.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, 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), 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)) ⊦ n0 = m0, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

User applied rule apply lemma

And obtained the following new goals

Proof step 27:
⊦ n0 < # apebs ∧ n1 < # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn)
Proof step 28:
# 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

Rule argument

spec: sqns name: valid-sqns-extract2-sqn seq: ⊦ n0 < # apebs ∧ n1 < # apebs ∧ n0 ≠ n1 ∧ valid-peb(v, m, apebs[n0]) ∧ valid-peb(v, m, apebs[n1]) → (∃ bag. valid-sqns(v, m, apebs) = bag ++ apebs[n0].vidhdr.sqn ++ apebs[n1].vidhdr.sqn) subst: [n0, apebs, n1, v, m] → [m0, apebs, n0, VTBL_VOLID, VTBL_LNUM]

Additional information

Used terms: m0, apebs, n0, VTBL_VOLID, VTBL_LNUM