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Proof step 113 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), 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, 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⌝ , vols[v][m] = unmapped → eq-entry(n, v × m) ∈ q, avols0[v][m].mapped? → # avols0[v][m].data = LEB_SIZE ∧ avols0[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols0[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols0[v][m].data, avols0[v][m].fill, emptyleb, 0, LEB_SIZE - avols0[v][m].fill) ⊦ 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 cut formula

And obtained the following new goals

Proof step 114:
# vols[v] = # vols0[v], # avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, vols[v][m] = unmapped, 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), 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, avols0[v][m].mapped? → # avols0[v][m].data = LEB_SIZE ∧ avols0[v][m].fill ≤ LEB_SIZE ∧ is-aligned(avols0[v][m].fill, EB_PAGE_SIZE) ∧ range=(avols0[v][m].data, avols0[v][m].fill, emptyleb, 0, LEB_SIZE - avols0[v][m].fill), vols[v][m] = unmapped → eq-entry(n, v × m) ∈ q, 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 ⊦ 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

fma: vols[v][m] ≠ unmapped

Additional information

Used simplifier rules: ⊦ ⌜m⌝ .pnum = m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)% ⊦ unmapped ≠ ⌜m⌝ ; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s) Used formulas: vols[v][m] ≠ unmapped