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Proof step 49 from proof recovery (previous step)

# vols[v] = # vols0[v], # wlar = # wlar0, # apebs0 = # wlar0, # avols0[v] = # vols0[v], vols[v][m] = unmapped, apebs0[unmapped.pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), avols0[v][m] = erased, vols0[v][m] = ⌜n⌝ , m < # vols0[v], n < # wlar0, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), 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 ∈ avols0, v ∈ vols, v ∈ vols0, q0.lebrefs ⊆ q.lebrefs, vols0⌈vols, q⌉ ⊦ VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0, v × m ∈ q

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 50:
⊦ 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 51:
# avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, # vols[v] = # vols0[v], vols0[v][m] = ⌜n⌝ , avols0[v][m] = erased, apebs0[unmapped.pnum] = mkpeb(aehdr, avhdr, buf, m0, boolvar), vols[v][m] = unmapped, n < # wlar0, m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), ebm-cons(avols0), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), 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, v ∈ vols, v ∈ avols0, q0.lebrefs ⊆ q.lebrefs, ∀ 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 ⊦ v × m ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

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