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Proof step 21 from proof absexpt-pebs-write (previous step)

# vols[v0] = # avols[v0], wlar[n].status = used, vols[avhdr.vol][avhdr.leb] = ⌜n⌝ , vols[v0][m0] = ⌜n⌝ , avols[v0][m0] = mapped(buf0, m1), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), avhdr.valid?, m0 < # avols[v0], n < # apebs, n < # wlar, avhdr.leb < # vols[avhdr.vol], avhdr.vol ∈ vols, v0 ∈ avols, v0 ∈ vols, m3 ≤ m1, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ avhdr.vol ∨ m0 ≠ avhdr.leb ⊦ n = n0, buf0 = buf ∧ m2 ≤ m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
# vols[v0] = # avols[v0], wlar[n].status = used, apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), avols[v0][m0] = mapped(buf0, m1), vols[v0][m0] = ⌜n⌝ , vols[v1][m4] = ⌜n⌝ , avhdr = avidhdr(v1, m4, m5, m6, m7), avhdr.valid?, m4 < # vols[v1], n < # wlar, n < # apebs, m0 < # avols[v0], v0 ∈ vols, v0 ∈ avols, v1 ∈ vols, m3 ≤ m1, ∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0, v0 ≠ v1 ∨ m0 ≠ m4 ⊦ n = n0, buf0 = buf ∧ m2 ≤ m1

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] → [avhdr, v1, m4, m5, m6, m7]

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: avhdr, v1, m4, m5, m6, m7