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Proof step 14 from proof mapped-pebs-unmap (previous step)

wlar[n0].status = used, vols[apebs[n0].vidhdr.vol][apebs[n0].vidhdr.leb] = ⌜n0⌝ , vols[apebs[n0].vidhdr.vol][m1] = ⌜n⌝ , apebs[n0].vidhdr.valid?, m1 < # vols[apebs[n0].vidhdr.vol], n0 < # apebs, n0 < # wlar, apebs[n0].vidhdr.leb < # vols[apebs[n0].vidhdr.vol], apebs[n0].vidhdr.vol ∈ vols, ∀ 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 ≠ m0 ⊦ m1 = apebs[n0].vidhdr.leb, n0 = m0, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
wlar[n0].status = used, apebs[n0].vidhdr = avidhdr(v0, m2, m3, m4, m5), vols[v0][m1] = ⌜n⌝ , vols[v0][m2] = ⌜n0⌝ , apebs[n0].vidhdr.valid?, m2 < # vols[v0], n0 < # wlar, n0 < # apebs, m1 < # vols[v0], v0 ∈ vols, ∀ 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 ≠ m0 ⊦ m1 = m2, n0 = m0, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

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[n0].vidhdr, v0, m2, m3, m4, m5]

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[n0].vidhdr, v0, m2, m3, m4, m5