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Proof step 64 from proof prepost-init-vols-mappings (previous step)

# 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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 65:
# apebs = # wlar, # wlar0 = # wlar, wlar[n0] = wl-entry(m7, used), vols[v][m0] = ⌜n0⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, false), recs1[v × m0] = recovery-entry(m3, m4), avhdr0 = avidhdr(v, m0, m1, m5, m6), avhdr0.valid?, n0 < # wlar, m0 < # vols[v], 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-peb(mkpeb(aehdr0, avhdr0, buf0, m2, false)), 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), v ∈ vols, v × m0 ∈ recs1, q1 ⊆ q, recs1 ⊥ vols ⊦ m3 = n0, n0 = n, recs1 = ∅, n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, n0 ∈ q

Rule argument

spec: avidheader name: elim seq: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)) subst: [avhdr, v, m, m0, m1, m2] → [avhdr0, v, m0, m1, m5, m6]

Additional information

Used simplifier rules: ⊦ avhdr.valid? → ( ( ((v = avhdr.vol ∧ m = avhdr.leb) ∧ m0 = avhdr.sqn) ∧ m1 = avhdr.size) ∧ m2 = avhdr.checksum ↔ avhdr = avidhdr(v, m, m0, m1, m2)); (elim) Used terms: avhdr0, v, m0, m1, m5, m6