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Proof step 3 from proof delta-wear-leveling (previous step)

# apebs = # wlar, bflipset = ∅, wlar0 = wlar, 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), ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_wear_leveling_worker#(LEB_SIZE, EB_PAGE_SIZE; vols, wlar, q, bflipset, n0, n1, apebs; err)⟫ (err = ESUCCESS → Δ wlar < Δ wlar0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 4:
ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = LEB_SIZE, vtblpnum1 = EB_PAGE_SIZE, ubi-io-inv(apebs), vols0 = vols, apebs0 = apebs, q0 = q ⊦ ⟪ubi_wear_leveling_worker#(vtblpnum0, vtblpnum1; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ ( vols0 = vols ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols0 ∧ m < # vols0[v] ∧ vols0[v][m] ≠ unmapped ∧ vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][m].pnum) ∧ apebs[n].data = apebs0[vols0[v][m].pnum].data ∧ apebs[n].fill ≤ apebs0[vols0[v][m].pnum].fill ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m))))
Proof step 5:
# apebs = # wlar, EB_PAGE_SIZE = EB_PAGE_SIZE, LEB_SIZE = LEB_SIZE, apebs = apebs, apebs1 = apebs, bflipset = ∅, q = q, q1 = q, vols = vols, vols1 = vols, vtblpnum2 = LEB_SIZE, vtblpnum3 = EB_PAGE_SIZE, wlar0 = 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(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n0), valid-wl(apebs, wlar) ⊦ [ubi_wear_leveling_worker#(LEB_SIZE, EB_PAGE_SIZE; vols, wlar, q, bflipset, n0, n1, apebs; err)] ( ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ∧ 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: inv-wl-worker seq: ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum), vtblpnum0 = LEB_SIZE, vtblpnum1 = EB_PAGE_SIZE, ubi-io-inv(apebs), vols0 = vols, apebs0 = apebs, q0 = q ⊦ ⟪ubi_wear_leveling_worker# (vtblpnum0, vtblpnum1 ; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs ; err)⟫ ( ubi-cons(apebs, vols, wlar, q, bflipset, vtblpnum, sqnum) ∧ ubi-io-inv(apebs) ∧ ( vols0 = vols ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols0 ∧ m < # vols0[v] ∧ vols0[v][m] ≠ unmapped ∧ vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ id (apebs, apebs0, mapped-pebs(vols0) -- vols0[v][m].pnum) ∧ apebs[n].data = apebs0[vols0[v][m].pnum].data ∧ apebs[n].fill ≤ apebs0[vols0[v][m].pnum].fill ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)))) subst: [vtblpnum1, vtblpnum0, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err, vols0, apebs0, q0] → [EB_PAGE_SIZE, LEB_SIZE, apebs, n1, n0, bflipset, q, wlar, vols, err, vols, apebs, q] 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)