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Proof step 63 from proof prepost-init-vols-mappings (previous step)

# wlar0 = # wlar, # apebs = # wlar, v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m0] = ⌜n0⌝ ↔ stat = used ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v0 ∧ avhdr0.leb = m0 ∧ n0 ≠ n, recs1[v0 × m1] = recovery-entry(m5, m6), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs1[v0 × m0] = recovery-entry(m3, m4), wlar[n0] = wl-entry(m7, stat), m0 = m1, 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 ⊦ v0 × m0 ≠ v0 × m1 ∧ v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m1, ⌜m5⌝ ][m0] = ⌜n0⌝ ↔ v0 × m0 ∈ recs1 ∧ m3 = n0 ∨ m0 < # vols[v0] ∧ vols[v0][m0] = ⌜n0⌝ , recs1 = ∅, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 64:
# wlar0 = # wlar, # apebs = # wlar, recs1[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, false), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), vols[avhdr0.vol][avhdr0.leb] = ⌜n0⌝ , wlar[n0] = wl-entry(m7, used), avhdr0.valid?, avhdr0.leb < # vols[avhdr0.vol], n0 < # wlar, 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-peb(mkpeb(aehdr0, avhdr0, buf0, m2, false)), 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), avhdr0.vol × avhdr0.leb ∈ recs1, avhdr0.vol ∈ vols, q1 ⊆ q, recs1 ⊥ vols ⊦ m3 = n0, n0 = n, recs1 = ∅, n0 ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1

Rule argument

Additional information

Used simplifier rules: lf-valid-wl-not-erroneous: n < # wlar, stat ≠ erroneous ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ wlar[n] = wl-entry(m0, stat) ∧ valid-wl(apebs, wlar) → ¬ boolvar;%lf-used-valid-peb: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ apebs[n] = apeb ∧ valid-wl(apebs, wlar) → valid-peb(apeb);%lf-used-info: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ used ≠ erroneous; (s)% ⊦ recovery-entry(m, m0) = recovery-entry(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)% ⊦ m < # ebatbl → ebatbl[m, ebae][m] = ebae; (s)