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Proof step 15 from proof inv-erase-all (previous step)

# apebs1 = # wlar0, # apebs = # wlar, apebs2 = apebs, wlar1 = wlar, m < # wlar, bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), id(apebs, apebs1, mapped-pebs(vols)), ubi-io-inv(apebs), ubi-io-inv(apebs1), unique-sqns(apebs1), unique-sqns(apebs), valid-ebatbl(apebs1, wlar0, vols, vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum), valid-eraseq(q2), valid-eraseq(wlar0, q2), valid-eraseq(apebs1, q2), 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(apebs1, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs1, wlar0), valid-wl(apebs, wlar), eq-entry(m, lref) ∈ q2, q0 ⊆ q2 ⊦ ∀ 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)), vtblpnum = m, vtblpnum ∈ q2, VTBL_VOLID ∈ vols, vtblpnum ∈ q0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
# apebs = # wlar, # apebs1 = # wlar0, # apebs0 = # wlar, # wlar2 = # wlar, wlar2[m].status ≠ used, vtblpnum ≠ m, m < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs0, apebs1, mapped-pebs(vols)), id(apebs0, apebs, mapped-pebs(vols)), id(apebs, apebs1, mapped-pebs(vols)), id○(wlar2, wlar, m), id○(apebs0, apebs, m), ubi-io-inv(apebs0), 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 ∈ q0, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q2, err = ESUCCESS → unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar2, q0) ∧ valid-eraseq(apebs0, q0) ∧ bflipset-cons(bflipset, wlar2) ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum), err ≠ ESUCCESS → unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(wlar2, eq-entry(m, lref) ' + q0) ∧ valid-eraseq(apebs0, eq-entry(m, lref) ' + q0) ∧ bflipset-cons(bflipset, wlar2) ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum), err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟪q := eq-entry(m, lref) ' + q0; if err = ESUCCESS then q := q.tail⟫ ( unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar2, q) ∧ valid-eraseq(apebs0, q) ∧ bflipset-cons(bflipset, wlar2) ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum) ∧ q ⊆ q2 ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ¬ # q0 < (err = ESUCCESS ⊃ # q;0))

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ ns = ns; (s)%idexcept-size: ⊦ id○(wlar, wlar0, n) → # wlar = # wlar0; (forward) from specification array-copy[wlarray-base]%idexcept-size: ⊦ id○(apebs, apebs0, n) → # apebs = # apebs0; (forward) from specification array-copy[apebs]%idset-trans-intersect: ⊦ id(apebs2, apebs1, ns0) ∧ id(apebs1, apebs0, ns1) → id(apebs2, apebs0, ns0 ∩ ns1); (forward) from specification ubi-base