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Proof step 10 from proof inv-erase-worker (previous step)

# apebs = # wlar, vtblpnum ≠ m, bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(eq-entry(m, lref) ' + q0), valid-eraseq(wlar, eq-entry(m, lref) ' + q0), valid-eraseq(apebs, eq-entry(m, lref) ' + q0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q0 ⊦ ⟪ubi_erase_worker_helper#(m; wlar, apebs; err); q := eq-entry(m, lref) ' + q0; if err = ESUCCESS then q := q.tail⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs))

User applied rule insert program lemma

And obtained the following new goals

Proof step 11:
ubi-cons(apebs, vols, wlar, q0 + eq-entry(m, lref) ' + q1, bflipset, vtblpnum, sqnum), m < # wlar, ubi-io-inv(apebs), wlar = wlar0, apebs = apebs0 ⊦ ⟪ubi_erase_worker_helper#(m; wlar, apebs; err)⟫ ( (err = ESUCCESS → ubi-cons(apebs, vols, wlar, q0 + q1, bflipset, vtblpnum, sqnum)) ∧ (err ≠ ESUCCESS → ubi-cons(apebs, vols, wlar, q0 + eq-entry(m, lref) ' + q1, bflipset, vtblpnum, sqnum)) ∧ ubi-io-inv(apebs) ∧ wlar[m].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar0, m) ∧ id○(apebs, apebs0, m) ∧ id(apebs, apebs0, mapped-pebs(vols)))
Proof step 12:
# apebs = # wlar, apebs = apebs, apebs1 = apebs, bflipset0 = bflipset, lref0 = lref, m0 = m, q2 = [], q3 = q0, sqnum0 = sqnum, vols0 = vols, vtblpnum0 = vtblpnum, wlar = wlar, wlar1 = wlar, m < # wlar, bflipset-cons(bflipset, wlar), ubi-cons(apebs, vols, wlar, [] + eq-entry(m, lref) ' + q0, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(apebs, eq-entry(m, lref) ' + q0), valid-eraseq(wlar, eq-entry(m, lref) ' + q0), valid-eraseq(eq-entry(m, lref) ' + q0), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar) ⊦ [ubi_erase_worker_helper#(m; wlar, apebs; err)] ( (err = ESUCCESS → ubi-cons(apebs, vols0, wlar, q2 + q3, bflipset0, vtblpnum0, sqnum0)) ∧ (err ≠ ESUCCESS → ubi-cons(apebs, vols0, wlar, q2 + eq-entry(m0, lref0) ' + q3, bflipset0, vtblpnum0, sqnum0)) ∧ ubi-io-inv(apebs) ∧ wlar[m0].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar1, m0) ∧ id○(apebs, apebs1, m0) ∧ id(apebs, apebs1, mapped-pebs(vols0)) → ⟪q := eq-entry(m, lref) ' + q0; if err = ESUCCESS then q := q.tail⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum) ∧ ubi-io-inv(apebs))), vtblpnum = m, VTBL_VOLID ∈ vols, vtblpnum ∈ q0

Rule argument

spec: <toplevel> name: prepost-erase-worker-helper seq: ubi-cons (apebs, vols, wlar, q0 + eq-entry(m, lref) ' + q1, bflipset, vtblpnum, sqnum), m < # wlar, ubi-io-inv(apebs), wlar = wlar0, apebs = apebs0 ⊦ ⟪ubi_erase_worker_helper#(m; wlar, apebs; err)⟫ ( ( err = ESUCCESS → ubi-cons (apebs, vols, wlar, q0 + q1, bflipset, vtblpnum, sqnum)) ∧ ( err ≠ ESUCCESS → ubi-cons (apebs, vols, wlar, q0 + eq-entry(m, lref) ' + q1, bflipset, vtblpnum, sqnum)) ∧ ubi-io-inv(apebs) ∧ wlar[m].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar0, m) ∧ id○(apebs, apebs0, m) ∧ id(apebs, apebs0, mapped-pebs(vols))) subst: [m, apebs, wlar, err, vols, q0, lref, q1, bflipset, vtblpnum, sqnum, wlar0, apebs0] → [m, apebs, wlar, err, vols, [], lref, q0, bflipset, vtblpnum, sqnum, wlar, apebs] flags: <all paths>

Additional information

Used simplifier rules: ⊦ [] + q = q; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]%⊦ 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)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ valid-eraseq(wlar, eq-entry(m, lref) ' + q1) → ¬ # wlar ≤ m; (s)