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Proof step 85 from proof recovery (previous step)

# apebs0 = # wlar0, # wlar = # wlar0, apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), vols0[v][m] = ⌜n⌝ , avhdr.valid?, m < # vols0[v], m < # absf(v, avols0[v], apebs0, vols0[v], q0, # 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 ∈ vols0, q0.lebrefs ⊆ q.lebrefs, vols ⊆ vols0, vols0⌈vols, q⌉, ∀ v. (v ∈ vols ↔ v ∈ avols0) ∧ ( v ∈ vols → # vols[v] = # avols0[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols0[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = apebs0[vols[v][m].pnum].data ∧ apebs0[vols[v][m].pnum].fill ≤ avols0[v][m].fill) ∧ (avols0[v][m] = erased → ¬ 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))

User applied rule all left

And obtained the following new goals

Proof step 86:
# wlar = # wlar0, # apebs0 = # wlar0, v ∈ vols ↔ v ∈ avols0, vols0[v][m] = ⌜n⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), avhdr.valid?, n < # wlar0, m < # absf(v, avols0[v], apebs0, vols0[v], q0, # vols0[v]), 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, vols ⊆ vols0, q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉, v ∈ vols → # vols[v] = # avols0[v] ∧ (∀ m. m < # vols[v] → (vols[v][m] = unmapped → ¬ avols0[v][m].mapped?) ∧ ( vols[v][m] ≠ unmapped → avols0[v][m].mapped? ∧ avols0[v][m].data = apebs0[vols[v][m].pnum].data ∧ apebs0[vols[v][m].pnum].fill ≤ avols0[v][m].fill) ∧ (avols0[v][m] = erased → ¬ v × m ∈ q)) ⊦ 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))

Rule argument

pos: left 34 terms: v abort: F discard: T computed: F

Additional information

Used terms: v