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Proof step 73 from proof vols-is-max-is-min-eraseq (previous step)

# apebs = # wlar1, # wlar0 = # wlar1, avhdr0.sqn = avhdr.sqn, wlar0[m0] = wl-entry(m3, erasing), apebs[n0] = mkpeb(aechdr(m6), avhdr, buf, m2, false), wlar1[m0] = wl-entry(m5, used), apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), wlar0[n0] = wl-entry(m6, used), valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs) = ∅ ++ avhdr.sqn ++ avhdr.sqn, n0 < # wlar1, m0 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar1), is-encoded(to-vtbl(vols0), buf), is-encoded(to-vtbl(vols1), buf0), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(apebs, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr, buf, m2, false)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), eq-entry(m0, VTBL_VOLID × VTBL_LNUM) ∈ q0, m0 ∈ q0, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])) ⊦ avhdr0 = empty, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1, VTBL_VOLID × VTBL_LNUM ∈ q1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ unique-sqns(apebs) ↔ (∀ v, m. unique-elems(valid-sqns(v, m, apebs)))
Proof step 75:
# wlar0 = # wlar1, # apebs = # wlar1, avhdr0.sqn = avhdr.sqn, wlar0[n0] = wl-entry(m6, used), apebs[m0] = mkpeb(aechdr(m5), avhdr0, buf0, m4, false), wlar1[m0] = wl-entry(m5, used), apebs[n0] = mkpeb(aechdr(m6), avhdr, buf, m2, false), wlar0[m0] = wl-entry(m3, erasing), valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs) = ∅ ++ avhdr.sqn ++ avhdr.sqn, m0 < # wlar1, n0 < # wlar1, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf0), is-encoded(to-vtbl(vols0), buf), valid-ebatbl(apebs, wlar0, vols0, n0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols0), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m5), avhdr0, buf0, m4, false)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr, buf, m2, false)), m0 ∈ q0, eq-entry(m0, VTBL_VOLID × VTBL_LNUM) ∈ q0, ∀ v. (v ∈ vols1 ↔ v ∈ vols0) ∧ (v ∈ vols1 → # vols1[v] = # vols0[v] ∧ (∀ m. m < # vols1[v] ∧ vols1[v][m] ≠ unmapped → vols1[v][m] = vols0[v][m])), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ avhdr0 = empty, VTBL_VOLID × VTBL_LNUM ∈ q1, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

Rule argument

spec: ubi-base name: unique-sqns seq: ⊦ unique-sqns(apebs) ↔ (∀ v, m. unique-elems(valid-sqns(v, m, apebs))) subst: [apebs] → [apebs] flags: <all paths>

Additional information

Used terms: apebs