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Proof step 3 from proof valid-ebatbl-map (previous step)

vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb] = unmapped, apebs[n].vidhdr.valid?, apebs[n].vidhdr.leb < # vols[apebs[n].vidhdr.vol], n < # apebs, n < # wlar, apebs[n].vidhdr.vol ∈ vols ⊦ wlar[n].status = used, (∀ v, m, n1. vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜n⌝ ]] ∧ m < # vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜n⌝ ]][v] ↔ wlar[n, wl-entry(m0, used)][n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0) ↔ (∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0), n = n0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
apebs[n].vidhdr = avidhdr(v0, m1, m2, m3, m4), vols[v0][m1] = unmapped, apebs[n].vidhdr.valid?, n < # wlar, n < # apebs, m1 < # vols[v0], v0 ∈ vols ⊦ wlar[n].status = used, (∀ v, m, n1. vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ wlar[n, wl-entry(m0, used)][n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0) ↔ (∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0), n = n0

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[n].vidhdr, v0, m1, m2, m3, m4]

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[n].vidhdr, v0, m1, m2, m3, m4