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Proof step 9 from proof delta-wear-leveling (previous step)

# apebs = # wlar, bflipset = ∅, ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n0), valid-wl(apebs, wlar), ¬ VTBL_VOLID ∈ vols ⊦ [ubi_get_pebs_for_wl#(wlar; vtblpnum0, vtblpnum, bflipset; boolvar); wlar0 := wlar; vols1 := vols; q1 := q; apebs1 := apebs; if boolvar then let avhdr = ?, bitflips = ? in {aubi_io_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); if err = ESUCCESS then let buf = mkbuf(LEB_SIZE) in {aubi_io_read_data#(vtblpnum, 0, 0, LEB_SIZE, apebs; buf; bitflips, err); if err = ESUCCESS then ubi_atomic_leb_change# (avhdr.vol, avhdr.leb, vtblpnum0, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, n0, n1, apebs; err); if err ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum.toString + " to PEB " + vtblpnum0.toString + " failed"); if err = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum; wlar, apebs; err); if err = ESUCCESS then q := q.butlast}}} else err := ENOSPC] ( # 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(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0) ∧ 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))) → err = ESUCCESS → Δ wlar < Δ wlar0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 10:
ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), bflipset0 = bflipset ⊦ ⟪ubi_get_pebs_for_wl#(wlar; n, m, bflipset; boolvar)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ( boolvar → n < # wlar ∧ wlar[n].status = free ∧ m < # wlar ∧ wlar[m].status = used ∧ (bflipset0 = ∅ → wlar[n].ec ≥ wlar[m].ec + WL_THRESHOLD)))
Proof step 11:
# apebs = # wlar, apebs0 = apebs, bflipset = ∅, bflipset = bflipset, bflipset1 = bflipset, q0 = q, sqnum0 = n1, vols0 = vols, vtblpnum1 = n0, wlar1 = wlar, ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n0), valid-wl(apebs, wlar) ⊦ [ubi_get_pebs_for_wl#(wlar; vtblpnum0, vtblpnum, bflipset; boolvar)] ( ubi-cons(apebs0, vols0, wlar1, q0, bflipset, vtblpnum1, sqnum0) ∧ ( boolvar → vtblpnum0 < # wlar1 ∧ wlar1[vtblpnum0].status = free ∧ vtblpnum < # wlar1 ∧ wlar1[vtblpnum].status = used ∧ (bflipset1 = ∅ → wlar1[vtblpnum0].ec ≥ wlar1[vtblpnum].ec + WL_THRESHOLD)) → [wlar0 := wlar; vols1 := vols; q1 := q; apebs1 := apebs; if boolvar then let avhdr = ?, bitflips = ? in {aubi_io_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); if err = ESUCCESS then let buf = mkbuf(LEB_SIZE) in {aubi_io_read_data#(vtblpnum, 0, 0, LEB_SIZE, apebs; buf; bitflips, err); if err = ESUCCESS then ubi_atomic_leb_change# (avhdr.vol, avhdr.leb, vtblpnum0, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, n0, n1, apebs; err); if err ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum.toString + " to PEB " + vtblpnum0.toString + " failed"); if err = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum; wlar, apebs; err); if err = ESUCCESS then q := q.butlast}}} else err := ENOSPC] ( # 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(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0) ∧ 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))) → err = ESUCCESS → Δ wlar < Δ wlar0)), VTBL_VOLID ∈ vols

Rule argument

spec: ubi-asm name: prepost-get-pebs-for-wl seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), bflipset0 = bflipset ⊦ ⟪ubi_get_pebs_for_wl#(wlar; n, m, bflipset; boolvar)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ( boolvar → n < # wlar ∧ wlar[n].status = free ∧ m < # wlar ∧ wlar[m].status = used ∧ ( bflipset0 = ∅ → wlar[n].ec ≥ wlar[m].ec + WL_THRESHOLD))) subst: [wlar, bflipset, m, n, boolvar, apebs, vols, q, vtblpnum, sqnum, bflipset0] → [wlar, bflipset, vtblpnum, vtblpnum0, boolvar, apebs, vols, q, n0, n1, bflipset] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # 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(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)% ⊦ bflipset-cons(∅, wlar); (s)