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Proof step 135 from proof inv-wl-worker (previous step)

# wlar2 = # wlar, # apebs0 = # wlar, # apebs = # wlar, # wlar0 = # wlar, # apebs1 = # wlar, apebs0[vtblpnum1] = mkpeb(aehdr1, avhdr, buf0, m2, boolvar0), apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum2] = wl-entry(m1, used), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs[vtblpnum2] = mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false), vols[v][m] = ⌜vtblpnum2⌝ , wlar2[vtblpnum2] = wl-entry(m5, stat), aehdr.valid?, vtblpnum2 < # wlar, m < # vols[v], vtblpnum1 < # wlar, bflipset-cons(bflipset1, wlar2), bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar0), id(apebs0, apebs, ((mapped-pebs(vols) -- vtblpnum2) ++ vtblpnum1) ∩ mapped-pebs(vols)), id(apebs1, apebs, mapped-pebs(vols)), id(apebs0, apebs1, (mapped-pebs(vols) -- vtblpnum2) ++ vtblpnum1), id(apebs0, apebs, mapped-pebs(vols) -- vtblpnum2 -- vtblpnum1), id○(apebs1, apebs, vtblpnum1), id○(apebs0, apebs1, vtblpnum2), id○(wlar2, wlar0, vtblpnum2), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false)), ubi-io-peb-inv(mkpeb(aehdr1, avhdr, buf0, m2, boolvar0)), unique-sqns(apebs0), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs0, wlar2, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-ebatbl(apebs1, wlar0, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], vtblpnum), valid-eraseq(apebs0, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(wlar2, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs1, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(wlar0, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(q + eq-entry(vtblpnum2, v × m) '), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum0), valid-peb(v, m, mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false)), valid-peb(mkpeb(aechdr(m1), avidhdr(v1, m4, valid-sqns(v, m, apebs).max, m6, m7), buf, m3, false)), valid-vtbl(apebs0, vols, wlar2, vtblpnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs0, wlar2), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), v ∈ vols, ⌊err⌋ , bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0 ⊦ stat = used, vtblpnum = vtblpnum2, vtblpnum2 = vtblpnum4, vtblpnum4 = vtblpnum1, VTBL_VOLID ∈ vols, vtblpnum4 ∈ q, vtblpnum2 ∈ q, vtblpnum ∈ q, vols = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] ∧ id(apebs0, apebs, (mapped-pebs(vols) -- vtblpnum2) ++ vtblpnum1) ∧ q.lebrefs ++ (v × m) ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM), id(apebs0, apebs, mapped-pebs(vols) -- vtblpnum2) ∧ buf0 = buf ∧ m2 ≤ m3

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-union, inst: nat-set name: del-in seq: ⊦ ¬ n ∈ ns → ns -- n = ns subst: [n, ns] → [vtblpnum1, mapped-pebs(vols) -- vtblpnum2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)% ⊦ used ≠ free; (s)%n < # wlar, stat ≠ used ⊦ wlar[n] = wl-entry(m, stat) ∧ valid-ebatbl(apebs, wlar, vols, n0) → ¬ n ∈ mapped-pebs(vols); (s) Used terms: vtblpnum1, mapped-pebs(vols) -- vtblpnum2