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Proof step 27 from proof refine-erase (previous step)

# apebs = # wlar0, wlar0[n] = wl-entry(m, stat), vols[v][vtblpnum2] = ⌜n⌝ , apebs1 = apebs, q = q0 + eq-entry(n, v × vtblpnum2) ', wlar = wlar0[n, wl-entry(m, erasing)], avols[v][vtblpnum2].mapped?, vtblpnum2 < # vols[v], vtblpnum2 < # avols[v], n < # wlar0, abs(avols, apebs, vols, q0), bflipset-cons(bflipset -- n, wlar0), bflipset-cons(bflipset, wlar0), ebm-cons(avols), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols, vtblpnum1), valid-ebatbl(apebs, wlar0[n, wl-entry(m, erasing)], vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq(apebs, q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(wlar0[n, wl-entry(m, erasing)], q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(q0 + eq-entry(n, v × vtblpnum2) '), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar0[n, wl-entry(m, erasing)], vtblpnum1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar0[n, wl-entry(m, erasing)]), v ∈ vols, v ∈ avols ⊦ ∀ wlar, q, apebs, err. # 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) ∧ ¬ VTBL_VOLID ∈ vols[v, vols[v][vtblpnum2, unmapped]] ∧ bflipset-cons(bflipset -- vols[v][vtblpnum2].pnum, wlar) ∧ valid-ebatbl(apebs, wlar, vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum1) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols[v, vols[v][vtblpnum2, unmapped]])) ∧ q ⊆ q0 + eq-entry(n, v × vtblpnum2) ' ∧ (err = ESUCCESS → q = []) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) → ⟨ebm_erase#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs, vols[v, vols[v][vtblpnum2, unmapped]], q) ∧ err = err0), VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# apebs = # wlar0, # apebs0 = # wlar1, wlar0[n] = wl-entry(m, stat), vols[v][vtblpnum2] = ⌜n⌝ , avols[v][vtblpnum2].mapped?, vtblpnum2 < # vols[v], vtblpnum2 < # avols[v], n < # wlar0, abs(avols, apebs, vols, q0), bflipset-cons(bflipset -- n, wlar0), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset -- n, wlar1), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- n), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols, vtblpnum1), valid-ebatbl(apebs, wlar0[n, wl-entry(m, erasing)], vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-ebatbl(apebs0, wlar1, vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-eraseq(apebs0, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq(apebs, q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(wlar0[n, wl-entry(m, erasing)], q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(q0 + eq-entry(n, v × vtblpnum2) '), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar0[n, wl-entry(m, erasing)], vtblpnum1), valid-vtbl(apebs0, vols, wlar1, vtblpnum1), valid-wl(apebs0, wlar1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar0[n, wl-entry(m, erasing)]), v ∈ vols, v ∈ avols, q1 ⊆ q0 + eq-entry(n, v × vtblpnum2) ', ¬ VTBL_VOLID ∈ vols, err = ESUCCESS → q1 = [], err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨ebm_erase#(v, vtblpnum2; avols; err0)⟩ (abs(avols, apebs0, vols[v, vols[v][vtblpnum2, unmapped]], q1) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ .pnum = m; (s)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)%⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ∧ valid-ebatbl(apebs, wlar, vols, m0) → mapped-pebs(vols[v, vols[v][m, unmapped]]) = mapped-pebs(vols) -- n0; (s)