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Proof step 187 from proof delta-wear-leveling (previous step)

# buf1 = # buf, # apebs = # wlar, apebs[vtblpnum2] = mkpeb(aehdr, avhdr0, buf0, m2, false), wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum2] = wl-entry(m1, used), apebs1 = apebs, buf = mkbuf(LEB_SIZE), err = err0, n = LEB_SIZE, n0 = 0, q1 = q, vols1 = vols, wlar0 = wlar, vtblpnum1 < # wlar, vtblpnum2 < # wlar, bflipset-cons(bflipset0, wlar), range=(buf1, 0, buf, 0, n0), range=(buf1, n0 + n, buf, n0 + n, # buf - n0 + n), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf0, 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, # buf1 = # buf → range=(buf1, 0, buf, 0, n0) → # buf ≥ n0 + n, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum2; wlar, apebs; err); if err = 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))) → err = ESUCCESS → Δ wlar < Δ wlar0), err = ESUCCESS, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 188:
# buf1 = LEB_SIZE, # apebs = # wlar, apebs[vtblpnum2] = mkpeb(aehdr, avhdr0, buf0, m2, false), wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum2] = wl-entry(m1, used), vtblpnum1 < # wlar, vtblpnum2 < # wlar, bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf0, 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, ⌊err0⌋ , ¬ VTBL_VOLID ∈ vols ⊦ [debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); wlar0 := wlar; q1 := q; apebs1 := apebs; 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) ∧ bflipset-cons(bflipset0, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n2) ∧ valid-vtbl(apebs, vols, wlar, n2) ∧ ubi-io-inv(apebs) ∧ ( id(apebs, apebs1, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] ≠ unmapped ∧ vols = vols[v, vols[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs1, mapped-pebs(vols) -- vols[v][m].pnum) ∧ apebs[n].data = apebs1[vols[v][m].pnum].data ∧ apebs[n].fill ≤ apebs1[vols[v][m].pnum].fill ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m))) → err0 = ESUCCESS → Δ wlar < Δ wlar0)

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ 0 ≤ m; (s)% ⊦ m ≤ m; (s)% ⊦ range=(buf, n0, buf0, n1, 0) ↔ n0 ≤ # buf ∧ n1 ≤ # buf0; (s)% ⊦ m - m = 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # mkbuf(n) = n; (s)