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Proof step 13 from proof inv-erase-all (previous step)

# apebs = # wlar, # apebs1 = # wlar0, apebs = apebs, apebs2 = apebs, bflipset0 = bflipset, lref0 = lref, m0 = m, q3 = [], q4 = q0, sqnum0 = sqnum, vols0 = vols, vtblpnum0 = vtblpnum, wlar = wlar, wlar1 = wlar, m < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs, apebs1, mapped-pebs(vols)), ubi-cons(apebs, vols, wlar, [] + eq-entry(m, lref) ' + q0, bflipset, vtblpnum, sqnum), ubi-io-inv(apebs1), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-ebatbl(apebs1, wlar0, 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-eraseq(apebs1, q2), valid-eraseq(wlar0, q2), valid-eraseq(q2), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), eq-entry(m, lref) ∈ q2, q0 ⊆ q2 ⊦ [ubi_erase_worker_helper#(m; wlar, apebs; err)] ( (err = ESUCCESS → ubi-cons(apebs, vols0, wlar, q3 + q4, bflipset0, vtblpnum0, sqnum0)) ∧ (err ≠ ESUCCESS → ubi-cons(apebs, vols0, wlar, q3 + eq-entry(m0, lref0) ' + q4, bflipset0, vtblpnum0, sqnum0)) ∧ ubi-io-inv(apebs) ∧ wlar[m0].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar1, m0) ∧ id○(apebs, apebs2, m0) ∧ id(apebs, apebs2, 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) ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q ⊆ q2 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ¬ # q0 < (err = ESUCCESS ⊃ # q;0))), vtblpnum = m, vtblpnum ∈ q2, VTBL_VOLID ∈ vols, vtblpnum ∈ q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# apebs = # wlar, # apebs1 = # wlar0, apebs2 = apebs, wlar1 = wlar, vtblpnum ≠ m, m < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs, apebs1, mapped-pebs(vols)), ubi-io-inv(apebs1), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-ebatbl(apebs1, wlar0, 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-eraseq(apebs1, q2), valid-eraseq(wlar0, q2), valid-eraseq(q2), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), eq-entry(m, lref) ∈ q2, q0 ⊆ q2, ¬ vtblpnum ∈ q2, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q0 ⊦ [ubi_erase_worker_helper#(m; wlar, apebs; err)] ( ( err = ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar, q0) ∧ valid-eraseq(apebs, q0) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum)) ∧ ( err ≠ ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, eq-entry(m, lref) ' + q0) ∧ valid-eraseq(apebs, eq-entry(m, lref) ' + q0) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum)) ∧ ubi-io-inv(apebs) ∧ wlar[m].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar1, m) ∧ id○(apebs, apebs2, m) ∧ id(apebs, apebs2, mapped-pebs(vols)) → ⟪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) ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q ⊆ q2 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ¬ # q0 < (err = ESUCCESS ⊃ # q;0)))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ 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)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ [] + q = q; (s)