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Proof step 126 from proof inv-recover (previous step)

# wlar = # wlar0, # wlar1 = # wlar0, # apebs0 = # wlar0, wlar0.mapIndices(nx, λ wle. wle.ec:= 0)[n] = wl-entry(m, stat), apebs0[m1] = mkpeb(aehdr, avhdr, buf1, m0, false), recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m1, avhdr.sqn), nx < # wlar0, m1 < # wlar0, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar1), indices-erasing(wlar, nx), is-encoded(vtbl, buf1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), unique-sqns(apebs0), unmapped-vols(vols0), valid-ebatbl(apebs0, wlar0, vols, m1), valid-ebatbl(apebs0, wlar1, vols1, m1), valid-eraseq(wlar0, q0), valid-eraseq(wlar, q), valid-eraseq(apebs0, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs0, vtbl, q0), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum5), valid-indices(wlar0, nx), valid-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols, wlar0, m1), valid-vtbl(apebs0, vols0, wlar, m1), valid-vtbl(apebs0, vols1, wlar1, m1), valid-vtbl-weak(apebs0, m1), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar1), VTBL_VOLID × VTBL_LNUM ∈ recs0, n ∈ bflipset2, q ⊆ q0, ∀ n. n ∈ bflipset2 → n < # wlar0 ∧ wlar0[n].status = used ⊦ # bflipset2 = 0, bflipset2 = ∅, dups(nx), VTBL_VOLID ∈ vols1, m1 ∈ q, VTBL_VOLID ∈ vols0, m1 ∈ q1, VTBL_VOLID ∈ vols, m1 ∈ q0, n < # wlar0.mapIndices(nx, λ wle. wle.ec:= 0) ∧ stat = used

User applied rule all left

And obtained the following new goals

Proof step 127:
# apebs0 = # wlar0, # wlar1 = # wlar0, # wlar = # wlar0, recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m1, avhdr.sqn), apebs0[m1] = mkpeb(aehdr, avhdr, buf1, m0, false), wlar0.mapIndices(nx, λ wle. wle.ec:= 0)[n] = wl-entry(m, stat), m1 < # wlar0, nx < # wlar0, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), indices-erasing(wlar, nx), is-encoded(vtbl, buf1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf1, m0, false)), unique-sqns(apebs0), unmapped-vols(vols0), valid-ebatbl(apebs0, wlar1, vols1, m1), valid-ebatbl(apebs0, wlar0, vols, m1), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-eraseq(wlar, q), valid-eraseq(wlar0, q0), valid-eraseq-strong(apebs0, vtbl, q0), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, vtblpnum5), valid-global-sqn(apebs0, sqnum), valid-indices(wlar0, nx), valid-recs(apebs0, wlar, recs0), valid-recs-sqns(apebs0, recs0), valid-vtbl(apebs0, vols1, wlar1, m1), valid-vtbl(apebs0, vols0, wlar, m1), valid-vtbl(apebs0, vols, wlar0, m1), valid-vtbl-weak(apebs0, m1), valid-wl(apebs0, wlar1), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), n ∈ bflipset2, VTBL_VOLID × VTBL_LNUM ∈ recs0, q ⊆ q0, n ∈ bflipset2 → n < # wlar0 ∧ wlar0[n].status = used ⊦ # bflipset2 = 0, bflipset2 = ∅, dups(nx), m1 ∈ q0, VTBL_VOLID ∈ vols, m1 ∈ q1, VTBL_VOLID ∈ vols0, m1 ∈ q, VTBL_VOLID ∈ vols1, n < # wlar0.mapIndices(nx, λ wle. wle.ec:= 0) ∧ stat = used

Rule argument

pos: left 42 terms: n abort: F discard: T computed: T

Additional information

Used terms: n