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Proof step 51 from proof refine-erase (previous step)

# apebs0 = # wlar1, # apebs = # wlar0, vols[v][vtblpnum2] = ⌜n⌝ , wlar0[n] = wl-entry(m, stat), avols[v][vtblpnum2].mapped?, n < # wlar0, vtblpnum2 < # avols[v], vtblpnum2 < # vols[v], abs(avols, apebs, vols, q0), bflipset-cons(bflipset -- n, wlar1), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset -- n, wlar0), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols) -- n), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-ebatbl(apebs, wlar0[n, wl-entry(m, erasing)], vols[v, vols[v][vtblpnum2, unmapped]], vtblpnum1), valid-ebatbl(apebs, wlar0, vols, vtblpnum1), valid-eraseq(q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(wlar0[n, wl-entry(m, erasing)], q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(apebs, q0 + eq-entry(n, v × vtblpnum2) '), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs0, q1), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar1, vtblpnum1), valid-vtbl(apebs, vols, wlar0[n, wl-entry(m, erasing)], vtblpnum1), valid-vtbl(apebs, vols, wlar0, vtblpnum1), valid-wl(apebs, wlar0[n, wl-entry(m, erasing)]), valid-wl(apebs, wlar0), valid-wl(apebs0, wlar1), v ∈ avols, v ∈ vols, q1 ⊆ q0 + eq-entry(n, v × vtblpnum2) ', ⌊err1⌋ ⊦ abs(avols, apebs0, vols[v, vols[v][vtblpnum2, unmapped]], q1), abs(avols[v, avols[v][vtblpnum2, unmapped]], apebs0, vols[v, vols[v][vtblpnum2, unmapped]], q1), abs(avols[v, avols[v][vtblpnum2, unmapped]], apebs0, vols[v, vols[v][vtblpnum2, unmapped]], q0 + eq-entry(n, v × vtblpnum2) '), VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-abs name: abs-idset-fwd seq: ⊦ id(apebs1, apebs0, mapped-pebs(vols)) ∧ valid-ebatbl(apebs0, wlar, vols, n0) ∧ abs(avols, apebs0, vols, q) → abs(avols, apebs1, vols, q) subst: [apebs0, wlar, n0, q, vols, apebs1, avols] → [apebs, wlar0[n, wl-entry(m, erasing)], vtblpnum1, q0 + eq-entry(n, v × vtblpnum2) ', vols[v, vols[v][vtblpnum2, unmapped]], apebs0, avols[v, avols[v][vtblpnum2, unmapped]]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 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)%⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → valid-ebatbl (apebs, wlar[n, wl-entry(m0, erasing)], vols[v, vols[v][m, unmapped]], n0); (ss)%⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ abs(avols, apebs, vols, q) → abs (avols[v, avols[v][m, unmapped]], apebs, vols[v, vols[v][m, unmapped]], q + eq-entry(n, v × m) '); (ss)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base] Used terms: apebs, wlar0[n, wl-entry(m, erasing)], vtblpnum1, q0 + eq-entry(n, v × vtblpnum2) ', vols[v, vols[v][vtblpnum2, unmapped]], apebs0, avols[v, avols[v][vtblpnum2, unmapped]]