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Proof step 15 from proof refine-erase-worker (previous step)

# apebs = # wlar, apebs1 = apebs, wlar1 = wlar, m < # wlar, abs(avols, apebs, vols, eq-entry(m, lref) ' + q0), bflipset-cons(bflipset, wlar), ebm-cons(avols), 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) ⊦ ∀ 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, apebs1, m) ∧ id(apebs, apebs1, mapped-pebs(vols)) → ⟪q := eq-entry(m, lref) ' + q0; if err = ESUCCESS then q := q.tail⟫ ⟨skip⟩ abs(avols, apebs, vols, q), VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%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]%abs-idset-fwd: ⊦ id(apebs1, apebs0, mapped-pebs(vols)) ∧ valid-ebatbl(apebs0, wlar, vols, n0) ∧ abs(avols, apebs0, vols, q) → abs(avols, apebs1, vols, q); (forward) from specification ubi-abs