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Proof step 99 from proof recovery (previous step)

# wlar = # wlar0, # apebs0 = # wlar0, # avols0[v] = # vols0[v], # vols[v] = # vols0[v], vols0[v][m] = ⌜n⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), apebs0[vols[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), avhdr.valid?, n < # wlar0, m < # vols0[v], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m0, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum0), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), v ∈ vols0, v ∈ vols, v ∈ avols0, q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉, avols0[v][m] = erased → ¬ v × m ∈ q, vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = buf0 ∧ m1 ≤ avols0[v][m].fill, vols[v][m] = unmapped → ¬ avols0[v][m].mapped?, vols[v][m] ≠ unmapped → vols[v][m] = ⌜n⌝ ⊦ VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0) ≤ LEB_SIZE ∧ is-aligned((avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0), EB_PAGE_SIZE) ∧ range=(buf, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0), emptyleb, 0, LEB_SIZE - (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 100:
⊦ vols1⌈vols0, q0⌉ ↔ (∀ v, m. v ∈ vols0 ∧ v ∈ vols1 ∧ m < # vols0[v] ∧ m < # vols1[v] ∧ vols0[v][m] = unmapped ∧ vols1[v][m] ≠ unmapped → eq-entry(vols1[v][m].pnum, v × m) ∈ q0)
Proof step 101:
# vols[v] = # vols0[v], # avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, apebs0[vols[v][m].pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), vols0[v][m] = ⌜n⌝ , avhdr.valid?, m < # vols0[v], n < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m0, false)), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs0, vtblpnum0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), v ∈ avols0, v ∈ vols, v ∈ vols0, q0.lebrefs ⊆ q.lebrefs, vols[v][m] ≠ unmapped → vols[v][m] = ⌜n⌝ , vols[v][m] = unmapped → ¬ avols0[v][m].mapped?, vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = buf0 ∧ m1 ≤ avols0[v][m].fill, avols0[v][m] = erased → ¬ v × m ∈ q, ∀ v, m. v ∈ vols ∧ v ∈ vols0 ∧ m < # vols[v] ∧ m < # vols0[v] ∧ vols[v][m] = unmapped ∧ vols0[v][m] ≠ unmapped → eq-entry(vols0[v][m].pnum, v × m) ∈ q ⊦ VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0) ≤ LEB_SIZE ∧ is-aligned((avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0), EB_PAGE_SIZE) ∧ range=(buf, (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0), emptyleb, 0, LEB_SIZE - (avols0[v][m].mapped? ⊃ avols0[v][m].fill;m0))

Rule argument

spec: ubi-crash-recovery-base name: vols-eraseq-bound seq: ⊦ vols1⌈vols0, q0⌉ ↔ (∀ v, m. v ∈ vols0 ∧ v ∈ vols1 ∧ m < # vols0[v] ∧ m < # vols1[v] ∧ vols0[v][m] = unmapped ∧ vols1[v][m] ≠ unmapped → eq-entry(vols1[v][m].pnum, v × m) ∈ q0) subst: [q0, vols0, vols1] → [q, vols, vols0] flags: <all paths>

Additional information

Used terms: q, vols, vols0