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Proof step 15 from proof valid-ebatbl-unmap (previous step)

wlar[n].status = used, vols[avhdr.vol][m] = ⌜n⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m3, boolvar), vols[avhdr.vol][avhdr.leb] = ⌜n⌝ , avhdr.valid?, n < # wlar, m < # vols[avhdr.vol], n < # apebs, avhdr.leb < # vols[avhdr.vol], avhdr.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 ≠ n0 ⊦ avhdr.leb = m, n = n0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
wlar[n].status = used, vols[v0][m0] = ⌜n⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m3, boolvar), vols[v0][m] = ⌜n⌝ , avhdr = avidhdr(v0, m0, m1, m2, m4), avhdr.valid?, m0 < # vols[v0], n < # apebs, m < # vols[v0], n < # wlar, 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 ≠ n0 ⊦ m0 = m, 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] → [avhdr, v0, m0, m1, m2, 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: avhdr, v0, m0, m1, m2, m4