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Proof step 32 from proof vols-is-max-is-max-vols (previous step)

# vols0[apebs[m5].vidhdr.vol] = # vols1[apebs[m5].vidhdr.vol], # apebs = # wlar1, # wlar0 = # wlar1, avhdr.leb = VTBL_LNUM, wlar1[m5].status = used, avhdr.vol = VTBL_VOLID, wlar0[m0] = wl-entry(m3, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar1[m0] = wl-entry(m4, used), ⌜m5⌝ = vols1[apebs[m5].vidhdr.vol][apebs[m5].vidhdr.leb], apebs[m5].vidhdr.valid?, m0 < # wlar1, apebs[m5].vidhdr.leb < # vols1[apebs[m5].vidhdr.vol], m5 < # wlar1, bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset1, wlar1), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(apebs, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs, q1), valid-eraseq(wlar1, q1), valid-eraseq(q1), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs, m1), valid-wl(apebs, wlar0), valid-wl(apebs, wlar1), apebs[m5].vidhdr.vol ∈ vols0, apebs[m5].vidhdr.vol ∈ vols1 ⊦ m5 = m0, ⌜m5⌝ = vols0[apebs[m5].vidhdr.vol][apebs[m5].vidhdr.leb], VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
# wlar0 = # wlar1, # apebs = # wlar1, # vols0[v] = # vols1[v], avhdr.leb = VTBL_LNUM, wlar1[m5].status = used, apebs[m5].vidhdr = avidhdr(v, m, m6, m7, m8), avhdr.vol = VTBL_VOLID, wlar1[m0] = wl-entry(m4, used), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar0[m0] = wl-entry(m3, used), ⌜m5⌝ = vols1[v][m], apebs[m5].vidhdr.valid?, m5 < # wlar1, m < # vols1[v], m0 < # wlar1, bflipset-cons(bflipset1, wlar1), bflipset-cons(bflipset0, wlar0), is-encoded(to-vtbl(vols1), buf), unique-sqns(apebs), valid-ebatbl(apebs, wlar0, vols0, m0), valid-eraseq(q1), valid-eraseq(wlar1, q1), valid-eraseq(apebs, q1), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs, q0), valid-eraseq-strong(apebs, to-vtbl(vols1), q0), valid-global-sqn(apebs, m1), valid-global-sqn(apebs, n1), valid-wl(apebs, wlar1), valid-wl(apebs, wlar0), v ∈ vols1, v ∈ vols0 ⊦ m5 = m0, ⌜m5⌝ = vols0[v][m], VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols0

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, v, m, m6, m7, m8]

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, v, m, m6, m7, m8