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Proof step 64 from proof delta-wear-leveling (previous step)

# apebs = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, apebs[n2] = mkpeb(aehdr, avhdr0, buf1, m2, false), wlar[vtblpnum1] = wl-entry(m0, free), wlar[n2] = wl-entry(m1, used), apebs1 = apebs, n4 = n2, q1 = q, vols1 = vols, wlar0 = wlar, vtblpnum1 ≠ n2, vtblpnum1 < # wlar, n2 < # wlar, bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf1, m2, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n2), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n2), valid-wl(apebs, wlar), m1 + WL_THRESHOLD ≤ m0, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_atomic_leb_change# (avhdr0.vol, avhdr0.leb, vtblpnum1, LEB_SIZE, copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, n2, n1, apebs ; err0)] ( Δ wlar = Δ wlar0 ∧ ecs(wlar) = ecs(wlar0) ∧ (err0 = ESUCCESS → wlar[vtblpnum1].ec = wlar0[vtblpnum1].ec ∧ wlar[n4].ec = wlar0[n4].ec) → [vtblpnum2 := n4; if err0 ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err0 = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum2; wlar, apebs; err0); if err0 = ESUCCESS then q := q.butlast}] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset0, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n2) ∧ valid-vtbl(apebs, vols, wlar, n2) ∧ ubi-io-inv(apebs) ∧ ( vols1 = vols ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols1 ∧ m < # vols1[v] ∧ vols1[v][m] ≠ unmapped ∧ vols = vols1[v, vols1[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs1, mapped-pebs(vols1) -- vols1[v][m].pnum) ∧ apebs[n].data = apebs1[vols1[v][m].pnum].data ∧ apebs[n].fill ≤ apebs1[vols1[v][m].pnum].fill ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m))) → err0 = ESUCCESS → Δ wlar < Δ wlar0))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 65:
# apebs = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, wlar[n2] = wl-entry(m1, used), wlar[vtblpnum1] = wl-entry(m0, free), apebs[n2] = mkpeb(aehdr, avhdr0, buf1, m2, false), wlar0[vtblpnum1] = wl-entry(m3, stat), apebs1 = apebs, n4 = n2, q1 = q, vols1 = vols, wlar0 = wlar, n2 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf1, m2, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n2), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n2), valid-wl(apebs, wlar), m1 + WL_THRESHOLD ≤ m0 ⊦ [ubi_atomic_leb_change# (avhdr0.vol, avhdr0.leb, vtblpnum1, LEB_SIZE, copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, n2, n1, apebs ; err0)] ( Δ wlar = Δ wlar0 ∧ ecs(wlar) = ecs(wlar0) ∧ (err0 = ESUCCESS → wlar[vtblpnum1].ec = m3 ∧ wlar[n4].ec = wlar0[n4].ec) → [vtblpnum2 := n4; if err0 ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err0 = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum2; wlar, apebs; err0); if err0 = ESUCCESS then q := q.butlast}] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset0, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n2) ∧ valid-vtbl(apebs, vols, wlar, n2) ∧ ubi-io-inv(apebs) ∧ ( vols1 = vols ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols1 ∧ m < # vols1[v] ∧ vols1[v][m] ≠ unmapped ∧ vols = vols1[v, vols1[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs1, mapped-pebs(vols1) -- vols1[v][m].pnum) ∧ apebs[n].data = apebs1[vols1[v][m].pnum].data ∧ apebs[n].fill ≤ apebs1[vols1[v][m].pnum].fill ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m))) → err0 = ESUCCESS → Δ wlar < Δ wlar0)), vtblpnum1 = n2, VTBL_VOLID ∈ vols

Rule argument

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar0[vtblpnum1], m3, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar0[vtblpnum1], m3, stat