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Proof step 42 from proof refine-erase (previous step)

# 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(wlar1, []), 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 ⊦ abs(avols[v, avols[v][vtblpnum2, erased]], apebs0, vols[v, vols[v][vtblpnum2, unmapped]], []), abs(avols[v, avols[v][vtblpnum2, erased]], apebs, vols[v, vols[v][vtblpnum2, unmapped]], []), VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-abs name: abs-erase-emptyq seq: ⊦ v ∈ vols ∧ m < # vols[v] ∧ abs(avols, apebs, vols, q) ∧ vols0 = vols[v, vols[v][m, unmapped]] → abs(avols[v, avols[v][m, erased]], apebs, vols0, []) subst: [vols, q, vols0, apebs, m, v, avols] → [vols, q0, vols[v, vols[v][vtblpnum2, unmapped]], apebs, vtblpnum2, v, avols] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ avols ∧ abs(avols, apebs, vols, q) → v ∈ vols; (ss)%⊦ v ∈ avols ∧ m < # avols[v] ∧ abs(avols, apebs, vols, q) → m < # vols[v]; (ss) Used terms: vols, q0, vols[v, vols[v][vtblpnum2, unmapped]], apebs, vtblpnum2, v, avols