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Proof step 210 from proof inv-recover (previous step)

# wlar1 = # wlar0, # wlar = # wlar0, # wlar0 = # wlar0.mapIndices(nx, λ wle. wle.ec:= 0), # apebs0 = # wlar0, avhdr0.sqn = valid-sqns(v, m6, apebs0).max, apebs0[m2] = mkpeb(aechdr(m7), avhdr0, buf, m, false), wlar0.mapIndices(nx, λ wle. wle.ec:= 0)[m2] = wl-entry(m4, used), wlar0[m2] = wl-entry(m7, used), vols[v][m6] = ⌜m2⌝ , recs0[VTBL_VOLID × VTBL_LNUM] = recovery-entry(m1, avhdr.sqn), apebs0[m1] = mkpeb(aehdr, avhdr, buf1, m0, false), vols1[v][m6] = unmapped, wlar1[m2] = wl-entry(m7, used), m1 < # wlar0, nx < # wlar0, m2 < # wlar0, m6 < # vols[v], m6 < # vols1[v], bflipset-cons(bflipset2, wlar0.mapIndices(nx, λ wle. wle.ec:= 0)), bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset2, wlar0), indices-erasing(wlar, nx), is-encoded(vtbl0, buf1), is-max(apebs0, vols, wlar0.mapIndices(nx, λ wle. wle.ec:= 0), q0, bflipset2, m1, sqnum), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aechdr(m7), avhdr0, buf, m, false)), 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, wlar0.mapIndices(nx, λ wle. wle.ec:= 0), vols, m1), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-eraseq(wlar, q), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(wlar0.mapIndices(nx, λ wle. wle.ec:= 0), q0), valid-eraseq(apebs0, q0), valid-eraseq-strong(apebs0, vtbl0, q0), valid-eraseq-stronger(apebs0, q), valid-global-sqn(apebs0, vtblpnum5), valid-global-sqn(apebs0, sqnum), valid-indices(wlar0, nx), valid-peb(v, m6, mkpeb(aechdr(m7), avhdr0, buf, m, false)), 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(apebs0, vols, wlar0.mapIndices(nx, λ wle. wle.ec:= 0), m1), valid-vtbl-weak(apebs0, m1), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0.mapIndices(nx, λ wle. wle.ec:= 0)), VTBL_VOLID × VTBL_LNUM ∈ recs0, v ∈ vols, v ∈ vols1, q ⊆ q0, ∀ v0, m3, n. vols1[v0][m3] = ⌜n⌝ ∧ v0 ∈ vols1 ∧ m3 < # vols1[v0] ↔ wlar1[n].status = used ∧ n < # wlar0 ∧ apebs0[n].vidhdr.valid? ∧ apebs0[n].vidhdr.vol = v0 ∧ apebs0[n].vidhdr.leb = m3 ∧ n ≠ m1 ⊦ avhdr0 = empty, m2 = m1, dups(nx), m1 ∈ q0, VTBL_VOLID ∈ vols, m1 ∈ q1, VTBL_VOLID ∈ vols0, m1 ∈ q, VTBL_VOLID ∈ vols1, eq-entry(m2, v × m6) ∈ q1, m2 ∈ q0

User applied rule all left

And closed the goal!

Rule argument

pos: left 61 terms: v, m6, m2 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ unmapped ≠ ⌜m⌝ ; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.valid?; (ss)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s) Used terms: v, m6, m2