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Proof step 156 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # apebs, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), q0 = q1, recs = ∅, recs2 = recs0 -- (VTBL_VOLID × VTBL_LNUM), vtblpnum = n, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq(wlar, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, vtblpnum), valid-wl(apebs, wlar0), valid-wl(apebs, wlar), q1 ⊆ q, recs ⊥ vols, ∀ v, m, n. v × m ∈ recs ∧ recs[v × m].pnum = n ∨ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ↔ wlar[n].status = used ∧ n < # apebs ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ vtblpnum, ∃ vtbl. is-encoded(vtbl, apebs[vtblpnum].data) ∧ valid-eraseq-strong(apebs, vtbl, q) ⊦ n ∈ q1, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs, VTBL_VOLID ∈ vols, valid-ebatbl(apebs, wlar, vols, n) ∧ valid-vtbl(apebs, vols, wlar, n) ∧ ¬ VTBL_VOLID ∈ vols ∧ # apebs = # wlar ∧ bflipset-cons(bflipset, wlar) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, q) ∧ q0 ⊆ q ∧ (∃ vtbl. is-encoded(vtbl, buf) ∧ valid-eraseq-strong(apebs, vtbl, q))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 157:
# wlar0 = # wlar, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar0, q1), valid-eraseq(wlar, q), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols0, wlar0, n), valid-vtbl(apebs, vols, wlar, n), valid-wl(apebs, wlar0), valid-wl(apebs, wlar), q1 ⊆ q, ∅ ⊥ vols, ∀ v, m0, n0. v ∈ vols ∧ m0 < # vols[v] ∧ vols[v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m0 ∧ n0 ≠ n ⊦ valid-ebatbl(apebs, wlar, vols, n), n ∈ q1, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ is-encoded(vtbl0, buf) → (is-encoded(vtbl1, buf) ↔ vtbl0 = vtbl1); (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ ¬ ladr ∈ ∅; (s)