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Proof step 56 from proof valid-ebatbl-remap (previous step)

wlar[n1].status = used, wlar[n2] = wl-entry(m8, used), wlar[n] = wl-entry(m9, stat0), apebs[n2] = mkpeb(aehdr0, avidhdr(apebs[n1].vidhdr.vol, apebs[n1].vidhdr.leb, m1, m2, m10), buf0, m7, boolvar0), apebs[n] = mkpeb(aehdr, avidhdr(apebs[n1].vidhdr.vol, apebs[n1].vidhdr.leb, m3, m4, m5), buf, m6, boolvar), vols[apebs[n1].vidhdr.vol][apebs[n1].vidhdr.leb] = ⌜n1⌝ , apebs[n1].vidhdr.valid?, n2 < # wlar, n2 < # apebs, n < # wlar, n < # apebs, n1 < # apebs, n1 < # wlar, apebs[n1].vidhdr.leb < # vols[apebs[n1].vidhdr.vol], apebs[n1].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 ≠ n0 ⊦ n = n0, n1 = n0, n2 = n0, n2 = n1, n2 = n, stat0 = used

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 57:
wlar[n1].status = used, apebs[n1].vidhdr = avidhdr(v0, m0, m11, m12, m13), vols[v0][m0] = ⌜n1⌝ , apebs[n] = mkpeb(aehdr, avidhdr(v0, m0, m3, m4, m5), buf, m6, boolvar), apebs[n2] = mkpeb(aehdr0, avidhdr(v0, m0, m1, m2, m10), buf0, m7, boolvar0), wlar[n] = wl-entry(m9, stat0), wlar[n2] = wl-entry(m8, used), apebs[n1].vidhdr.valid?, m0 < # vols[v0], n1 < # wlar, n1 < # apebs, n < # apebs, n < # wlar, n2 < # apebs, n2 < # 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 ⊦ n = n0, n1 = n0, n2 = n, n2 = n1, n2 = n0, stat0 = used

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[n1].vidhdr, v0, m0, m11, m12, m13]

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[n1].vidhdr, v0, m0, m11, m12, m13