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Proof step 71 from proof refine-erase (previous step)

# apebs0 = # wlar0, # apebs = # wlar, unmapped = vols[v][vtblpnum2], vtblpnum2 < # avols[v], vtblpnum2 < # vols[v], abs(avols, apebs, vols, q), abs(avols, apebs0, vols, q), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar), ebm-cons(avols), id(apebs0, apebs, mapped-pebs(vols)), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar0, vols, vtblpnum1), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-eraseq(wlar0, []), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar0), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols ⊦ avols[v][vtblpnum2].mapped?, abs(avols[v, avols[v][vtblpnum2, erased]], apebs0, vols, []), 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, q, vols, apebs0, 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)% ⊦ ebatbl[n] = ebae → ebatbl[n, ebae] = ebatbl; (s)% ⊦ v ∈ vols → vols[v, vols[v]] = vols; (s) Used terms: vols, q, vols, apebs0, vtblpnum2, v, avols