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Proof step 54 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), m1 < # vols[v0], 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), v0 × m1 ∈ recs1, v0 ∈ vols, q1 ⊆ q, recs1 ⊥ vols, ∀ v, m, n0. v × m ∈ recs1 ∧ recs1[v × m].pnum = n0 ∨ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m ∧ n0 ≠ n ⊦ v × m0 ≠ v0 × m1 ∧ v × m0 ∈ recs1 ∧ recs1[v × m0].pnum = n0 ∨ v ∈ vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]] ∧ m0 < # vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]][v] ∧ vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]][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, recs1 = ∅, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 55:
# apebs = # wlar, # wlar0 = # wlar, apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), m1 < # vols[v0], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-encoded(vtbl, buf), unique-sqns(apebs), unmapped-vols(vols0), valid-eraseq(wlar, q), valid-eraseq(wlar0, q1), valid-eraseq-strong(apebs, vtbl, q), valid-eraseq-stronger(apebs, q1), valid-recs(apebs, wlar0, recs0), valid-vtbl(apebs, vols, wlar, n), valid-vtbl(apebs, vols0, wlar0, n), valid-wl(apebs, wlar), valid-wl(apebs, wlar0), v0 ∈ vols, v0 × m1 ∈ recs1, q1 ⊆ q, recs1 ⊥ vols, ∀ v, m, n0. v × m ∈ recs1 ∧ recs1[v × m].pnum = n0 ∨ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m ∧ n0 ≠ n ⊦ v × m0 ≠ v0 × m1 ∧ v × m0 ∈ recs1 ∧ recs1[v × m0].pnum = n0 ∨ v ∈ vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]] ∧ m0 < # vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]][v] ∧ vols[v0, vols[v0][m1, ⌜recs1[v0 × m1].pnum⌝ ]][v][m0] = ⌜n0⌝ ↔ wlar[n0].status = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m0 ∧ n0 ≠ n, recs1 = ∅, n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[n0], aehdr0, avhdr0, buf0, m2, boolvar0]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[n0], aehdr0, avhdr0, buf0, m2, boolvar0