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Proof step 27 from proof valid-ebatbl-add-unmapped-vol (previous step)

wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2] = wl-entry(m4, used), wlar[n1] = wl-entry(m2, free), apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), avhdr.valid?, n2 < # apebs, n2 < # wlar, ∀ 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 ⊦ n2 = n1, v ∈ vols, vols[v, fill(mkebatbl(n), unmapped)][avhdr.vol][avhdr.leb] = ⌜n2⌝ ∧ avhdr.vol ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ avhdr.leb < # vols[v, fill(mkebatbl(n), unmapped)][avhdr.vol]

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
apebs[n2] = mkpeb(aehdr, avhdr, buf, m3, boolvar), wlar[n1] = wl-entry(m2, free), wlar[n1, wl-entry(m1, used)][n0, wl-entry(m0, erasing)][n2] = wl-entry(m4, used), avhdr = avidhdr(v0, m5, m6, m7, m8), avhdr.valid?, n2 < # wlar, n2 < # apebs, ∀ 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 ⊦ n2 = n1, v ∈ vols, vols[v, fill(mkebatbl(n), unmapped)][v0][m5] = ⌜n2⌝ ∧ v0 ∈ vols[v, fill(mkebatbl(n), unmapped)] ∧ m5 < # vols[v, fill(mkebatbl(n), unmapped)][v0]

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, m5, m6, m7, m8]

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, m5, m6, m7, m8