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Proof step 105 from proof prepost-init-vols-mappings (previous step)

# apebs = # wlar, # wlar0 = # wlar, wlar[m5] = wl-entry(m7, used), recs1[v × m0] = recovery-entry(m3, m4), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), recs1[apebs[m5].vidhdr.vol × apebs[m5].vidhdr.leb] = recovery-entry(m5, m6), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), apebs[m5].vidhdr.valid?, m5 < # wlar, 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), apebs[m5].vidhdr.vol × apebs[m5].vidhdr.leb ∈ recs1, q1 ⊆ q, q1 ⊆ q + eq-entry(m5, apebs[m5].vidhdr.vol × apebs[m5].vidhdr.leb) ', recs1 ⊥ vols ⊦ m5 = n, recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, apebs[m5].vidhdr.vol × apebs[m5].vidhdr.leb) '), n ∈ q1, VTBL_VOLID ∈ vols, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols0, m5 ∈ q, apebs[m5].vidhdr.vol ∈ vols ∧ apebs[m5].vidhdr.leb < # vols[apebs[m5].vidhdr.vol], valid-peb(apebs[m5].vidhdr.vol, apebs[m5].vidhdr.leb, apebs[m5]) ∧ (¬ apebs[m5].vidhdr.vol ∈ vtbl ∨ ¬ apebs[m5].vidhdr.leb < vtbl[apebs[m5].vidhdr.vol])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 106:
# wlar0 = # wlar, # apebs = # wlar, apebs[m5].vidhdr = avidhdr(v0, m1, m9, m10, m11), wlar[m5, wl-entry(m7, erasing)][n0] = wl-entry(m8, stat0), recs1[v0 × m1] = recovery-entry(m5, m6), apebs[n0] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs1[v × m0] = recovery-entry(m3, m4), wlar[m5] = wl-entry(m7, used), apebs[m5].vidhdr.valid?, m5 < # 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-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, q1 ⊆ q + eq-entry(m5, v0 × m1) ', q1 ⊆ q, recs1 ⊥ vols ⊦ m5 = n, recs1 = ∅, valid-eraseq-strong(apebs, vtbl, q + eq-entry(m5, v0 × m1) '), m5 ∈ q, VTBL_VOLID ∈ vols0, VTBL_VOLID × VTBL_LNUM ∈ recs1, VTBL_VOLID ∈ vols, n ∈ q1, valid-peb(v0, m1, apebs[m5]) ∧ (¬ v0 ∈ vtbl ∨ ¬ m1 < vtbl[v0]), v0 ∈ vols ∧ m1 < # vols[v0]

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] → [apebs[m5].vidhdr, v0, m1, m9, m10, m11]

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: apebs[m5].vidhdr, v0, m1, m9, m10, m11